The US Federal Aviation Administration has prohibited all airlines from flying from Turkey to the United States, as Secretary of State John Kerry told his counterpart that public claims suggesting the US was involved in the failed coup in Turkey were harmful to relations between the two NATO allies.

Mr Kerry's response came after Turkish President Recep Tayyip Erdogan called on US President Barack Obama to extradite an Islamic cleric accused of being the ringleader behind an attempted military coup that saw more than 150 people die and left more than 1500 injured. 

Turkey has long sought action against Fethullah Gulen, who's been living in the US for more than 15 years.

Mr Erdogan has said the cleric, who lives in self-imposed exile in the United States, is trying to build a "parallel structure" in the judiciary and army to try to overthrow the state, which Mr Gulen denies.

He addressed his American counterpart, Barack Obama, directly: "Dear Mr President, I told you this before. Either deport Fethullah Gulen or return him to Turkey. You didn't listen. I call on you again."

He said Turkey has been preparing a formal application with detailed information about Gulen's illegal activities.

In a meeting with Turkish Foreign Minister Mevlut Cavosoglu, Mr Kerry pressed Turkey to use restraint and respect the rule of law during its investigation into the plot, State Department spokesman John Kirby said in a statement.

"He made clear that the United States would be willing to provide assistance to Turkish authorities conducting this investigation, but that public insinuations or claims about any role by the United States in the failed coup attempt are utterly false and harmful to our bilateral relations," Mr Kirby said. 

Mr Gulen, who's based in Pennsylvania, denied any connection with the coup, which petered out on Saturday morning after a night of violence in the country's two biggest cities, Istanbul and Ankara.

"You can think about many motivations of people who staged this coup. They could be sympathisers of the opposition party. They could be sympathisers of the nationalist party. It could be anything," he said.

A Turkish official said the death toll from the coup had risen to 265, including 161 mostly civilians and police officers, and 104 coup supporters. Nearly 1500 people were left injured. 

Authorities ordered 2745 judges and prosecutors be detained, broadcaster NTV said, and officials are promising to extend the purge.

As well as banning incoming flights from Turkey, the US FAA issued a notice banning US commercial and private aircraft from flying to Turkey.

Mr Erdogan, who had been holidaying on the coast when the coup was launched, flew into Istanbul before dawn on Saturday and was shown on TV appearing among a crowd of supporters outside the airport, which the coup plotters had failed to secure.

He said those responsible would pay a heavy price. Arrests of officers were under way, he said, and it would go higher up the ranks, culminating in the cleansing of the military.

He said some military personnel were taking orders from Gulen, whose movement he called an armed terrorist organisation.

But Mr Gulen condemned the uprising and denied any involvement, saying "governments should be won through a process of free and fair elections, not force."

Soldiers who used tanks to blockade the Bosphorus Bridge in Istanbul surrendered and were photographed walking towards a group of President Erdogan's supporters with their hands up.

The head of Turkey's armed forces was taken hostage by his own soldiers during the attempted coup, and an acting chief of military was appointed. However, a senior Turkish official told Reuters military head Hulusi Akar has since been rescued.

Earlier on Saturday, US Secretary of State John Kerry said the US anticipates having "some discussion" with its NATO ally Turkey about extraditing Gulen.

"We invite the government of Turkey, as we always do, to present us with any legitimate evidence that withstands scrutiny, and the United States will accept that and look at it and make judgments about it appropriately," Kerry said.

Istanbul's international airport has reopened with Turkish Airlines resuming flights on Saturday. Some foreign carriers cancelled weekend flights.

The closure of Istanbul's Ataturk Airport late on Friday caused the diversion of 35 airplanes and cancelled 32 flights, Turkish Airlines chairman Ilker Ayci told broadcaster CNN Turk.

Reuters is quoting Greek military sources saying an anti-government group at Turkey's Golcuk Navel Base has taken over a frigate, holding the head of the Turkish fleet hostage.

And a Turkish military helicopter landed in Northern Greece and the eight men on board have been arrested, according to the Greek Police Ministry.

The eight arrested men have requested political asylum, the Greek Police Ministry said, but Turkey is demanding their return.

Prime minister Yildrim said they would consider the death penalty to punish the coup plotters.

He said although the death penalty was not in the country's constitution, but Turkey would consider legal changes to "make sure this doesn't happen again".

Turkey's president Recep Tayyip Erdogan said those behind the "act of treason" would be held responsible.

His government has moved swiftly to "clean up the army" and detain more than 2839 soldiers involved in the attempted uprising.

The country's head of armed forces was taken hostage, a military helicopter was shot down, tanks opened fire around Turkey's parliament building, bridges out of Istanbul were blockaded, and rebels stormed a news service during the bloody attempted coup.

But shortly after Mr Erdogan took to mobile app Facetime to urge supporters to take to the streets, the uprising started to lose momentum.

A total of 17 police officers were killed in the fighting when their offices in the Turkish capital of Ankara were fired on by a helicopter being used by the military faction trying to seize power.

Turkey Prime Minister Binali Yildirim said a group within the country's military attempted to overthrow the government and security forces were called in to "do what is necessary".

"Some people illegally undertook an illegal action outside of the chain of command," Mr Yildirim said in comments broadcast by private channel NTV on Friday, local time.

"The government elected by the people remains in charge. This government will only go when the people say so."

Those behind the attempted coup would pay the highest price, he added, as a no-fly-zone was declared over the Turkish capital Ankara.

The military said in a statement, sent by email and reported on Turkish TV channels, that the armed forces had taken power in the country to protect the democratic order and to maintain human rights.

All of Turkey's existing foreign relations would be maintained and the rule of law would remain the priority, it said.

One senior Turkish government official said the military faction behind the coup had taken control of some tanks and ordered its forces to try and take over the streets.

Footage on local television channels showed military vehicles blocking bridges over the Bosphorus in Istanbul and tanks deployed at the city's main airport. In the capital Ankara, warplanes and helicopters roared overhead. A Reuters journalist heard gunshots.

The office of broadcaster CNNTurk was stormed by insurgents, but the news service has since resumed its regular programming.

A Turkish official who did not want to be named said soldiers had been deployed in other cities in Turkey, but did not specify which ones.

Dogan News Agency reported the national police directorate had summoned all police to duty in Ankara.

President Tayyip Erdogan, who has ruled Turkey since 2003, would amount to one of the biggest shifts in power in the Middle East in years.

In an extraordinary mobile phone live-cross on television before flying back to Istanbul, President Erdogan reportedly said the uprising has come from a "minority" within the military.

Speaking by either Skype or Facetime, on a phone held up by a newsreader, he said the plotters would not succeed. AFP reports he told people to "take to the streets".

He has cut short a holiday to fly back to Istanbul.

Turkey, a NATO member with the second biggest military in the Western alliance, is one of the most important allies of the United States in the fight against Islamic State.

It is a principal backer of opponents of Syrian President Bashar al-Assad in that country's civil war, and host to two million Syrian refugees.

The Obama administration has expressed its support for Turkey's government, with Secretary of State John Kerry issuing the following statement:

"I spoke this evening to Foreign Minister Cavusoglu and emphasised the United States' absolute support for Turkey's democratically-elected civilian government and democratic institutions," he said.

German Chancellor Angela Merkel has also affirmed her support for Turkey's government.

The Department of Foreign Affairs issued a message to Australian citizens in Turkey, repeating the French and US calls for people to stay indoors.

"There are reports of unauthorised military movements in Ankara and Istanbul and gunfire. Bridges across the Bosphorous in Istanbul are closed. Airport operations have been disrupted, including at Istanbul's Ataturk airport," DFAT said.

"Confirm your flight's status before travelling to the airport so long as it is safe to do so. You should stay indoors and avoid unnecessary travel. Avoid any large gatherings or demonstrations. Follow the directions of local authorities.

"We continue to advise Australians to exercise a high degree of caution in Turkey overall and to reconsider their need to travel to Istanbul and Ankara. Higher levels apply in some parts of Turkey."

Flights to Turkey from Australia (via other destinations) are still operating today.

The commander of Turkey's special forces General Zekai Aksakalli said the armed forces did not support the coup that was being carried out by what the government described as a small military faction.

- Craig Butt, Neelima Choahan, Reuters, Bloomberg, LA Times