As Egypt struggles to reinvent itself, many experts in the region say that it might look to Turkey for some valuable lessons.

Arriving at a template that effectively integrates Islam, democracy and vibrant economics has been a near-impossible dream for Middle East reformers stretching back decades. To a large extent, Egypt’s inability to accommodate these three themes lies at the root of its current plight.

But no country in the region has come closer to accomplishing this trick, warts and all, than Turkey. As a result, diplomats and analysts have begun to present the still-incomplete Turkish experiment as a possible road map for Egypt.

“Turkey is the envy of the Arab world,” said Hugh Pope, project director for the Turkish office of the International Crisis Group. “It has moved to a robust democracy, has a genuinely elected leader who seems to speak for the popular mood, has products that are popular from Afghanistan to Morocco — including dozens of sitcoms dubbed into Arabic that are on TV sets everywhere — and an economy that is worth about half of the whole Arab world put together.”

The idea is not new. President Obama’s first trip as president to a Muslim country was to Turkey in April 2009, and he hailed its progress as a Middle East model. (His visit there preceded his better-remembered speech in Cairo by two months.)

Since then, the already wide distance separating these countries has grown. Turkey’s economy and its internationally competitive companies are expanding at a relentless pace. Meanwhile, its mildly Islamist prime minister, Recep Tayyip Erdogan, seems on a path to win his third election in a row, having effectively neutered a once-all-powerful military apparatus long seen as the guardian of secularism in the country.

It has not always been this way.

Indeed, when Hosni Mubarak came to power in Egypt in October 1981, after the assassination of President Anwar el-Sadat, Turkey was still being governed by its army, which one year earlier intervened to impose a sense of order on the country’s fractious political scene.

But while Mr. Mubarak, a military man himself, banked upon authoritarian rule, paying only lip service to democratic institutions and running rigged elections, the general behind the Turkish coup, Kenan Evren, moved to withdraw from politics. The constitution he imposed left the military considerable scope to meddle in political affairs, but it allowed civilian institutions to bloom.

On the economic front Egypt maintained state control, with many restrictions on foreign trade and domestic competition. By contrast, Turkey, which hopes to join the European Union, has opened up its economy and unleashed a dynamic private sector.

Today, with similarly sized populations of about 80 million, Turkey has an economy that is nearly four times the size of Egypt’s.

Its recent growth spurt has been driven by Mr. Erdogan, who came to power in 2003 and focused first on reducing deficits and bringing down inflation. Only after he demonstrated success in raising living standards did he feel confident enough to overcome opposition from the determinedly secular army and the cosmopolitan elite in Istanbul by introducing elements of Islam into Turkish public life.

He has been rewarded with broad popular support at home — demonstrated in September when Mr. Erdogan easily won a referendum that further diluted the military’s powers — and growing influence abroad.

In responding to the Egypt crisis, President Obama telephoned Prime Minister Erdogan twice in six days to discuss the unfolding events, and administration officials say they have been keeping in close contact with their Turkish counterparts at all levels.

“There’s no question that Turkey can play a role,” one administration official said. The official, speaking on grounds of anonymity, noted that Mr. Erdogan and Turkish leaders had publicly called for Mr. Mubarak to listen to what the protesters on the streets of Cairo had been saying — words that might have heartened democracy advocates in the Muslim world.

Turkey’s ability to thrive as a predominantly Muslim country that maintains diplomatic relations — though chilly — with Israel is one that American officials would like to see other Muslim nations develop.

But it is also true that actions taken by the Erdogan government against the Turkish news media have been a cause for some concern, a point made recently by the new American ambassador to Turkey, Francis J. Ricciardone Jr., who was ambassador to Egypt from 2005 to 2008.

With the Egyptian military likely to play the role of political guarantor in any transition from Mr. Mubarak’s rule, analysts suggest that Turkey might serve as a model for introducing new political parties, writing a constitution from scratch and ultimately stepping aside and letting the democratic process play out (as uncomfortable as that might be) — all of which the Turkish military has done since the 1980 coup.

“The military did not overplay its hand in Turkey,” said Soner Cagaptay, an analyst at the Washington Institute for Near East Policy. Mr. Cagaptay also said that even though Mr. Erdogan had made gains in pushing his Islamist agenda, the military served as an effective restraint.

“The relative moderation of Islamic parties in Turkey is due to the military,” he said.

There are still substantial differences between the countries. For the Turkish military, its organizing philosophy has always been preserving the secularist traditions that Turkey’s post-World War I founder, Kemal Ataturk, set in place. In Egypt, while the Muslim Brotherhood has been officially banned, the army has been seen more as the defender of the authoritarian status quo rather than secularism itself.

How the military in Egypt deals with the Muslim Brotherhood — by far the most powerful civic force in the country — will be crucial in determining the country’s political future.

Can it, as was the case in Turkey, encourage the formation of competing political parties? And can it encourage the moderate elements of the Muslim Brotherhood to come to the fore rather than its more militant factions?

Turkey may have a more direct role to play on that front. Mr. Erdogan’s party has already established ties to the Muslim Brotherhood — a result of Mr. Erdogan’s long and successful campaign to present himself as a dominant and increasingly anti-Israeli voice in the Middle East.

According to research by Dore Gold at the Jerusalem Center for Public Affairs, three members of the Muslim Brotherhood — two of whom serve in the Egyptian Parliament — were on the Turkish-sponsored ship that was attacked by Israeli forces on its way to deliver aid to the Gaza Strip in May.

“There is a great deal of ideological compatibility between the A.K.P. and the Muslim Brotherhood,” said Mr. Gold, a former top adviser to Prime Minister Benjamin Netanyahu of Israel, referring to Mr. Erdogan’s Justice and Development Party. “This is something to watch carefully.”

Perhaps, but in the end that could be a plus rather than a minus.

For all his Islamist sympathies, Mr. Erdogan is at root a pragmatist. As a young firebrand he was jailed for his antisecular rhetoric but now, after working within Turkey’s democratic framework rather than outside it, he is recognized as perhaps the Middle East’s most influential figure.