GAZIANTEP, Turkey — For a fleeting moment last year, Louai Abo Aljoud, a Syrian journalist, made eye contact with the American hostages being held by the Islamic State militant group.

One of dozens of prisoners inside a former potato chip factory in northern Syria, Mr. Abo Aljoud was taken out of his cell one day and assigned to deliver meals to fellow inmates. It was when he opened the slot to Cell No. 2 that he first saw them — the gaunt, frightened faces of James Foley, Steven J. Sotloff and Peter Kassig.

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Mr. Abo Aljoud, a 23-year-old freelance cameraman, said he resolved not only to save himself, but also to help the other inmates if he could. He memorized the prison’s floor plan and studied its location in Aleppo. When he became one of the lucky few to be released this May, he pressed to meet with American officials in neighboring Turkey.

“I thought that I had truly important information that could be used to save these people,” he said. “But I was deeply disappointed.”

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A State Department employee and a contractor were eventually sent to meet him at a restaurant, but both were assigned to deal with civil society in Syria, not hostages. Mr. Abo Aljoud grew frustrated, insisting he could pinpoint the location of the prison on a map. Instead, he said, he received only vague assurances that the employees would pass on the details he had shared and his contact information to the relevant investigators.

“It’s my impression that they were more interested in gathering intelligence, in general, than in saving these people,” he said. “I could have shown them the location on Google Maps, but they weren’t interested.” Although the hostages had been moved by the time he met with the American officials this spring, the militants have been known to recycle prison locations.

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The United States says that it does all it can through diplomacy, intelligence gathering and even military action, such as a failed commando raid in Syria in July, to try to free hostages. It reached out to more than two dozen countries to seek help in rescuing the Americans held in Syria, a National Security Council spokesman, Alistair Baskey, said in an emailed statement on Friday. Mr. Abo Aljoud offers a counterpoint to the official government position: one that does not contradict all of Washington’s assertions but indicates systemic gaps in its efforts to free captives.

The New York Times has previously reported that many European countries have funneled ransoms to terrorists to rescue their citizens, a tactic the United States has steadfastly refused to pursue, arguing that it encourages more kidnappings. But interviews with family members of the hostages, former F.B.I. officials, freed prisoners and Syrians claiming to be go-betweens for the Islamic State suggest that this policy has also made the government reluctant to engage with people claiming to have valuable information about the hostages or suggesting possible ways to free them.

The challenge of dealing with hostages has grown more acute and complicated over the past year with the rise of the Islamic State, also known as ISIS or ISIL, which has beheaded hostages from nations that have refused to pay ransoms.

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In the decade before the Sept. 11, 2001, terror attacks, the Federal Bureau of Investigation brought most American hostages home safely by engaging directly with the kidnappers. But after Al Qaeda struck, the approach changed as jihadists transformed kidnappings into a lucrative business that raised hundreds of millions of dollars in ransoms. The United States refused to pay and increasingly refused to consider even talking to the kidnappers, directly or indirectly, critics say.

Former F.B.I. officials say that the post-9/11 approach led to lost opportunities and, perhaps, lives.

“The policy of no concession has always been there, but we used to interpret it in a much more flexible way,” said Gary Noesner, who retired in 2003 as chief of the F.B.I.’s Crisis Negotiation Unit. “The problem in my mind is that we have devalued negotiation as a tool.”

Mr. Abo Aljoud’s account mirrors those of six other witnesses who were either present at the moments of the Americans’ abductions or were held alongside them. They describe going to lengths this spring and summer to give American officials information that they believed could help free the hostages. And they say they were disheartened by what they perceived as a lack of urgency on the part of those officials.

Similarly, several Syrian rebel commanders say that American officials rejected their proposals to act as go-betweens with the jihadists in war-torn Syria, often for a sizable cash fee, on the grounds that the United States does not negotiate with terrorists.

In one instance a few months before Mr. Foley was beheaded in August, a rebel fighter said he had brought an Islamic State sheikh here to Gaziantep, Turkey, about 35 miles north of the Syrian border, where a delegation of American officials was meeting. The sheikh had a letter from the group stating that he was authorized to negotiate — but the officials declined to talk with him.

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“They said: ‘We don’t meet with terrorists. How dare you bring a terrorist to see us?’ And the meeting was canceled,” said the rebel fighter, who requested anonymity because the Islamic State had not authorized him to speak to reporters. “ISIS knew that the Americans were not going to negotiate a ransom. That is why they began slaughtering them.”

Government officials said there was no blanket policy that would prevent investigators from speaking to people with credible information about or access to hostages. A senior F.B.I. official said that Mr. Abo Aljoud’s information would have been “of relatively little value” because it was four months old by the time he could have reported the prison location.

“There is no such directive against engaging intermediaries if they are credible and seem to have a legitimate ability to influence the captors,” a senior Obama administration official said Friday.

A Hotly Debated Policy

Relatives of the victims, as well as retired law enforcement officials who oversaw hostage negotiations under previous administrations, say the post-9/11 policy has meant not just that the government will not pay cash to kidnappers, but that it will not participate in any negotiations. Critics argue that this runs counter to longstanding instructions in the F.B.I.’s operations manual, which provides guidance on how agents can help families pay private ransoms.

They say, moreover, that the way the policy is currently applied is at odds with a classified 2002 presidential directive that allows the government to pay ransoms in special cases, so long as the money is used as a lure to catch the perpetrators, according to two officials who were involved in drafting the order.

“When you say that you will not make concessions to terrorists,” Mr. Noesner, the former F.B.I. agent, said, “there are some people who now believe this means we should not even talk to the kidnappers.”

An F.B.I. spokesman, Christos G. Sinos, said in an email that the agency’s approach to hostage negotiations abroad had been governed since 2002 by the presidential directive. Because the directive is classified, he could not confirm details, including whether ransoms were allowed in some cases.

“The F.B.I.’s top priority in international kidnapping investigations is the safe return of our citizens,” said Richard P. Quinn, section chief of the F.B.I.’s office of public affairs. “Because the circumstances are different in each case, the F.B.I. works closely with the rest of the U.S. government to consider all viable options to secure their release. To preserve these options, and out of respect for their loved ones, we rarely discuss these details publicly.”

As four Americans languished in the Islamic State’s network of jails in Syria, at least 15 hostages held alongside them were released. All but one were European, and they were freed after aggressive negotiations by their governments, employers and families, including the payment of ransoms.

Retired officials with decades of experience in hostage negotiations said there were a number of tools short of paying ransoms that Washington could have tried. For example, officials could have asked a third country to intervene, a role that Qatar often plays, or used diplomatic channels to push for an exchange of prisoners held elsewhere. France successfully persuaded Mali this month to free four members of Al Qaeda’s North African branch in return for the French hostage Serge Lazarevic.

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Another possibility would have been to allow the hostages’ families to pay ransoms themselves, as was the norm through the early 2000s, according to two former F.B.I. officials.

Instead, the family members of the four Americans say they were told they could be prosecuted if they paid.

Those who tried to do so anyway faced logistical challenges that proved insurmountable. The United States offered little guidance to the families, who were sometimes confronted with offers from swindlers posing as the kidnappers. Although Denmark, France, Germany, Italy and Spain all succeeded in getting their citizens released, and the United States has intelligence-sharing agreements with each of those countries, advocates for the American prisoners were not able to find out what channel the European negotiators had used to communicate with the militants.

In the desperate final weeks, the families themselves were thrust into the role of hostage negotiators. They worked with no training or access to classified information, with tragic results.

“As best I could determine, there were only two means to secure the release of Jim Foley and Steven Sotloff and Peter Kassig,” said Philip S. Balboni, the chief executive of GlobalPost, the online publication for which Mr. Foley worked as a freelance cameraman and reporter. “One was through negotiation with the kidnappers in return for some value, and two was a high-risk military mission to extract them. It seemed to me that the first course was the wisest — and we have the proof that 15 Europeans are now safe and well and home with their families.”

“There was no nuance applied to this problem,” Mr. Balboni added.

Mr. Baskey, the National Security Council spokesman, said that the government was aware of family members’ concerns about the way officials had interacted with them, and that this had prompted a review of the administration’s response to hostage cases.

“The government provides all of the information we can to families in these circumstances without jeopardizing our efforts to bring hostages home safely or putting at risk the critical intelligence sources we must protect to do so, and on which we depend to confront the terrorist groups who engage in this despicable conduct,” he said in an email on Friday.

When Hostages Came Home

For much of the 1990s and early 2000s, hostage negotiations were led exclusively by the F.B.I., whose role in such cases dates back to the kidnapping of the aviator Charles Lindbergh’s son in the 1930s.

From 1993 until his retirement in 2003, Mr. Noesner said he had free rein to handle overseas kidnappings. He and others say the unit had a 90 percent recovery rate because it engaged with the captors and had the flexibility to guide families on how to pay ransoms.

“We never gave the money ourselves, and we didn’t officially condone it, but if families wanted to pay, we gave them a wink and a nod,” Mr. Noesner said. “The State Department was not comfortable with what we were doing. And while our official justification for being there was to investigate the crime and try to make an arrest, the real success was getting the hostage out. Very rarely were we able to if a ransom wasn’t paid.”

Mr. Noesner and the agents working under him followed the protocol outlined in the F.B.I.’s Manual of Investigative Operations and Guidelines, which stated that the decision on whether to pay a ransom was to be made by the victim’s family, he said. That policy was designed for domestic kidnappings, but Mr. Noesner applied it to international cases as well. Mr. Sinos, the F.B.I. spokesman, declined to comment on whether that language was still included in the manual.

“That is the guidance I used to formulate our policy,” Mr. Noesner said. “We were enormously successful for a decade.” Then, he said, “along came 9/11.”

Mr. Noesner and another former F.B.I. agent said that after Sept. 11, 2001, the center of gravity shifted from direct negotiations to military solutions. The F.B.I. became just one of several agencies dealing with kidnappings.

As a result, families are often given contradictory guidance.

“All of the families went to Washington earlier this year,” said Nancy Curtis, the mother of Theo Padnos, who was held by the Syrian branch of Al Qaeda for nearly two years before his release this summer. “We went to the State Department, and they told us it’s against U.S. policy to negotiate with terrorists or to pay a ransom. Then we go to the F.B.I., and they say, ‘When we negotiate with terrorists, which we have done many times in the past, we will be sitting right next to you and helping you.’ So you think, ‘What’s going on here? Which message do I listen to?’ ”

Diane Foley, Mr. Foley’s mother, said that on three occasions, a National Security Council official told her family that they could be prosecuted if they paid a ransom. The family decided to begin fund-raising anyway, relying in part on the advice of Charles Regini, a 21-year veteran of the F.B.I. who is now a director at Unity Resources Group, the security company that led the search for Mr. Foley.

As a former F.B.I. hostage negotiator, Mr. Regini knew the agency had helped families arrange ransoms in the past. He also shared a little-known fact: The classified presidential directive that lays out how the government should deal with kidnappings includes an exception to the ban on paying ransoms.

The loophole, he said, allows the government to use a ransom as a lure to trap the kidnappers, with the goal of recovering the money. Mr. Regini said this could give the Obama administration leeway in interpreting the policy.

The only time the exception was applied, he said, was in a 2002 attempt to free two American missionaries held by Abu Sayyaf, a terrorist group in the Philippines. According to a now-retired official who was involved, the operation did not go well: One of the two Americans was killed, and only part of the $300,000 ransom was recovered.

“It’s the will of senior leaders: They can leverage a number of options at their disposal, and one of the options is paying a ransom, whether it’s paid by the family or paid by the government,” Mr. Regini said. “It’s not about whether or not they had the capability. It’s about not having the will.”

A Chilling Effect

In the shadowy underground that has grown up on the edges of Syria’s civil war, spies and fighters mingle in the cafes of cities like Gaziantep, where jihadists and their allies make a living selling tips to American operatives.

One of these fighters, a white-haired general who defected from the Syrian Air Force and now gathers intelligence for a group of rebels, said he had helped in the search for Mr. Foley.

The general, who asked not to be identified out of concern for his security, said he had been approached in February by an Islamic State commander who was looking for a way to leave the group. The man claimed he had access to a prison in Raqqa, Syria, where the hostages had been moved. He wanted $750,000 and a promise of asylum in the United States in return for smuggling Mr. Foley to Turkey.

The general said he sent an aide to the United States Embassy in Ankara, Turkey, to brief officials on the development.

He said he was disappointed by their response. “They didn’t even want to hear the details; they rejected the proposal outright,” he said. “The Americans just keep on saying, ‘We don’t negotiate with terrorists.’ ”

A spokesman at the embassy referred questions about the general’s visit to Washington. Officials in Washington would not comment on the specific episode.

Two other rebel fighters in Turkey, including one reportedly involved in the release of Danish, German and Italian hostages, recounted similar experiences.

Soon after the failed American raid in July, one fighter said, the Islamic State sent an envoy named Sheikh Abdullah al-Jarrah al-Nasir to Gaziantep over the summer with a letter authorizing him to negotiate on behalf of the group. The rebel, who asked not to be named, brought the sheikh here to see an American intelligence official whom he knew only as Darren. He said he was not sure if this was the official’s real name.

“I met Darren, and he came out, but he refused to meet Sheikh Abdullah,” the fighter said. “I told him, ‘The sheikh is here to negotiate.’ Darren blamed me and said, ‘We don’t meet with terrorists.’ I told him, ‘If you don’t meet with ISIS and deal with them as a state, this will end very badly.’ ”

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The Evolution of ISIS

Critics of the United States’ approach say it led to a kind of paralysis, where oftentimes leads were not investigated and sources were not interviewed, or else were interviewed too late.

Mr. Padnos, who was kidnapped by Al Qaeda’s Syrian affiliate, the Nusra Front, in October 2012, described how the three men who had grabbed him stole his iPhone 3. In the nearly two years he spent sitting in a cell, he imagined that his captors had erased the data from the phone to avoid detection. When he was finally freed after his family appealed to the government of Qatar, he got a new computer and signed in to iCloud, the online storage service he had used to back up data.

“When I put in my password into the iCloud, down came my old data I had from before and a bunch of new phone numbers that my kidnappers had inputted,” Mr. Padnos said.

His captors had been using his iPhone all along, yet it appears no investigators logged into his account or used it to track his whereabouts.

Others who came in contact with American hostages, including Syrians and Europeans held as prisoners alongside them, say they were tracked down and interviewed by representatives of the hostages’ families before anyone from the American government contacted them. Some said that they had been prepared to share important information, including the locations of the numerous jails where the hostages were held, and that they were baffled by the United States’ seemingly uninterested response.

Among them is Jejoen Bontinck, a 19-year-old Belgian convert to Islam. Mr. Bontinck went to Syria last year to join the jihad, only to run afoul of the militants, who accused him of being a spy and imprisoned him in the same cell as Mr. Foley.

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Upon his return to Antwerp, Belgium, in the fall of 2013, employees of the security company hired by GlobalPost to search for Mr. Foley flew to Europe to interview him. It was weeks, however, before the United States sent its own investigators. And months elapsed, he said, before the F.B.I. sent a sketch artist to ask Mr. Bontinck to describe the blue-eyed Dutch jihadist who ran the prison where he and the other hostages had been held for much of the summer of 2013.

“By the time the F.B.I. came to speak to me, Jim and the other hostages had already been moved to a different location,” Mr. Bontinck said.

An F.B.I. spokesman said that the United States had an intelligence-sharing agreement with the Belgian authorities and that it had gleaned information from Mr. Bontinck through them before it sent officials to meet him.

Mr. Regini, who worked at the F.B.I. for two decades, counters that the intelligence shared between governments was usually only a summary, not a substitute for the level of detail investigators can gather during an in-person interview.

Families as Negotiators

After months of seeing no progress, and after the unsuccessful American military raid in July, the hostages’ families tried to engage with the kidnappers themselves.

Their desperation grew with each beheading. By September, after Mr. Foley and Mr. Sotloff had been killed, Mr. Kassig’s family learned from a Syrian employee of The Times of a man who called himself Sheikh Mohamed and claimed to be a negotiator for the Islamic State.

Mr. Kassig’s parents in Indiana sent a 27-year-old friend of their son to meet with the sheikh on Sept. 22. They met inside a mall in Sanliurfa, Turkey, a short drive from the Syrian border. The sheikh had a cellphone picture of himself posing with the Danish hostage Daniel Rye Ottosen on the day of his release this summer.

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Mr. Ottosen, who spent months in the same cell as Mr. Kassig and the other Americans, had been freed after his family paid a ransom estimated at around 3.5 million euros, or about $4.3 million. His friends and family raised the money, and the Danish government arranged for it to be transferred to the jihadists, according to Mr. Regini. The United States did not provide such assistance. Civilians working to free the remaining American hostages were not able to determine whether, for example, the sheikh had really been involved in Mr. Ottosen’s release.

The sheikh began the discussion on Sept. 22 by saying that the Kassigs needed to pay $100,000 as proof that they were “committed” to the negotiations, according to three people present at the meeting. One of the sheikh’s associates said that the militants had intended to ask for around $20 million for Mr. Kassig, an aid worker. But they never got past the first step.

The family’s representative asked for a few days to consider the proposal.

After consulting with the Kassigs, he replied that without proof of the sheikh’s ability to secure Mr. Kassig’s release, they would not pay the $100,000, a sum that would have involved mortgaging their house. They suggested a recording of his voice, according to an associate of the sheikh, who, like two others who described details of the encounter, did not want to be identified for fear of angering the Islamic State.

Instead, the sheikh became enraged, the associate said, accusing the Americans of doubting his credentials.

The associate described the conversation that ensued: “The sheikh called me and said, ‘Tell the family they will see their proof of life on TV.’ ”

Eleven days after the meeting, a video was uploaded to YouTube showing Mr. Kassig kneeling next to his knife-wielding executioner.

Among the people who recognized Mr. Kassig’s pale face was Mr. Abo Aljoud, the Syrian freelance journalist, who had glimpsed his features through the slot in Cell No. 2.

Mr. Abo Aljoud said it was sheer luck that he had not been killed. Twice during his 158-day captivity, he was taken outside to be decapitated, only to be saved at the last moment when the jihadists recognized him as one of the captives being discussed for a prisoner exchange among rebel groups in Syria.

When he was finally freed and had a chance to report what he had seen, the American government sent a State Department employee and a contractor, according to Marie Harf, a State Department spokeswoman.

“These two individuals do not work on hostage-related issues, and this was made clear to Mr. Abo Aljoud,” Ms. Harf said in an email. “Any information they or anyone else may have received that was related to American hostages was passed on through appropriate channels. And any notion that there was one piece of information that could have brought U.S. citizens held hostage home is just not borne out by the facts.”

In the weeks that followed, Mr. Abo Aljoud said he waited for a call that never came.

“I always thought that the American president is powerful enough to reshape the map of the world,” he said. “I was disappointed to see that he couldn’t do so much as get these hostages out, knowing that even the smallest rebel brigade in Syria is able to get its people out.”