Turkish President Recep Tayyip Erdogan has flown in to Istanbul, after an army group said the country was taken over by it.
Sixty people died during 754 soldiers, many of them civilians, and overnight battles were arrested, officials said.
Prime Minister Binali Yildirim said the situation was mostly under control.
He has ordered the military to shoot down aircraft used by coup plotters.
Before, one of the choppers being flown by forces involved in the coup attempt was shot down over the capital Ankara.
He is reported to have been taken hostage by rebel soldiers.
Commander of the 1st Army, Gen Umit Dundar, continues to be appointed acting chief of staff.
Sporadic gunfire is still reported in major cities.
Reports also say rebel soldiers in some regions have been surrendering their weapons to police loyal to Mr Erdogan.
The surrender of one unit of 60 soldiers, who had taken control of the Bosphorus bridges of one in Istanbul, was revealed on TV on Saturday.
Istanbul’s main Ataturk airport is now under army control, and flights – which was interrupted for some hours – were due to resume from 06:00 (03:00 GMT).
In a statement, the Turkish foreign ministry said the coup attempt “was foiled by the Turkish people in unity and solidarity. Our president and authorities are in charge”.
“Turkish Armed Forces was not involved with the coup attempt in its entirety. It was conducted by a clique within the armed forces and received a well-deserved answer from our country.”
It’s not clear how much support it enjoys or who is leading the coup faction.
The group previously declared that a “peace council” now ran the nation and there was a curfew and martial law.