The state-run news agency said more than 750 soldiers had been detained.
However, fighting continued throughout the morning, with the sounds of huge blasts echoing across the capital Ankara and Istanbul, including at least one bomb that hit the parliament complex.
Government officials said the coup appeared to have failed as Turks took to the streets overnight to confront troops attempting to take over the country.
Addressing supporters outside Istanbul’s Ataturk Airport on Saturday morning, President Recep Tayyip Erdogan told the crowd assembled there: “They have pointed the people’s guns against the people. The president, whom 52% of the people brought to power, is in charge.
“This government brought to power by the people, is in charge. They won’t succeed as long as we stand against them by risking everything.”
Justice minister Bekir Bozdag said security forces have defeated coup plotters in several places, including police and government buildings, according to the state-run Anadolu news agency.
“There is nowhere they have they have proper control,” Mr Bozdag said. “God willing, they will be defeated in the remaining areas and those in the air will be brought down.”
It was not clear who was in control of the military headquarters and Mr Erdogan had not left the airport as dawn broke.
Earlier he said the government was arresting coup supporters in the military and warned “they will pay a heavy price for their treason to Turkey”, according to a transcript of his remarks provided by his office.
“Those who stain the military’s reputation must leave. The process has started today, and it will continue just as we fight other terrorist groups,” he said.
An official in the president’s office said at least 60 people had been killed and more than 330 arrested.
In images broadcast on CNN-Turk, dozens of soldiers walked among tanks with their hands up, surrendering to government forces on Istanbul’s Bosporus Bridge. Discarded gear was strewn on the ground and people, some holding flags, climbed on to the tanks.
Anadolu reported that 754 members of Turkey’s armed forces have been detained across the country. At the Etimesgut armoured units training command, in the outskirts of Ankara, some soldiers who took part in the attempted coup were arrested by fellow officers or soldiers and handed over to police, the agency said.
Mr Erdogan, who said his general secretary had been abducted by the coup plotters, flew into Ataturk early on Saturday and was greeted by large crowds. Hours earlier, as the coup attempt got under way, his office declined to say where he was and he was forced to give an interview over FaceTime to a television station.
Prime minister Binali Yildirim has called all MPs to an emergency meeting on Saturday, Anadolu reported.
The chaos capped a period of political turmoil in Turkey which critics blamed on Mr Erdogan’s increasingly authoritarian rule, which has included a government shake-up, a crackdown on dissidents and opposition media and renewed conflict in the mainly Kurdish areas of the south east.
Turkey, a Nato member, is a key partner in US-led efforts to defeat the Islamic State group and has allowed American jets to use its Incirlik air base to fly missions against the extremists in nearby Syria and Iraq.
A coup against the democratically-elected government could make it difficult for the United States to continue to co-operate with Turkey.
US president Barack Obama urged all sides in Turkey to support the democratically-elected government and Nato secretary general Jens Stoltenberg said he spoke to Turkish foreign minister Mevlut Cavusoglu and called for respect for democracy.
The coup attempt began on Friday night with a statement from the military saying it had seized control “to reinstall the constitutional order, democracy, human rights and freedoms, to ensure that the rule of law once again reigns in the country, for law and order to be reinstated”.
But the military did not appear unified, with top commanders taking to television to condemn the action and order troops back to their barracks.
Mr Erdogan called on Turks to take to the streets across the country, and many did, marching through the streets of Izmir and Istanbul, waving Turkish flags and gathering in the main square in Ankara.
At least 42 people were killed in the capital, NTV quoted the prosecutor’s office as saying. Parliament speaker Ismail Kahraman said a bomb hit one corner of a public relations building inside the parliament complex, injuring some police officers.
In Istanbul, an official at Haydarpasa Numune Hospital said at least 150 people were admitted with wounds but would not comment on whether there were fatalities. NTV reported six dead had been brought to that hospital.
An official at Istanbul’s Sisli Hamidiye Etfal Training and Research Hospital said they had also received dead and wounded.
In his TV address, Mr Erdogan blamed the attack on supporters of exiled cleric Fethullah Gulen.
Mr Erdogan has long accused the cleric and his supporters of attempting to overthrow the government. The cleric lives in exile in Pennsylvania and promotes a philosophy that blends a mystical form of Islam with staunch advocacy of democracy, education, science and interfaith dialogue.