Britons were advised to stay indoors following a night of gunfire and explosions in Ankara and Istanbul and reports of shooting near the tourist resort of Marmaris.
British Airways cancelled all flights to and from the country on Saturday and the Foreign Office said the security situation “remains potentially volatile”.
On Saturday evening a British Airways spokesman said: “We’ll be flying a reduced schedule to Turkey tomorrow (Sunday July 17), however these flights may be subject to some delays.
“We continue to keep our flights to Turkey under review and we recommend that customers check ba.com for the latest information.”
Thomas Cook had been advising customers to “stay in their hotels until further notice”, but a later statement from the company - which offers holidays to places such as Marmaris, Bodrum and Antalya - said: “Our flight and holiday programme is operating as normal and our staff on the ground in resort tell us that everything is calm and customers are enjoying their holidays.”
An easyJet spokeswoman said the airline did not expect any changes to its schedule, while Turkish Airlines advised passengers to check the latest flight information due to cancellations.
Thomson and First Choice flights to Dalaman, Antalya and Izmir are operating as normal.
Flight disruption meant a party of British schoolchildren were stranded at Istanbul Ataturk Airport after leaving Birmingham on Friday evening.
Some 41 students and seven members of staff from the Arthur Terry School in Sutton Coldfield were stuck at the airport since their connecting flight to South Africa was grounded.
Advice on the Foreign Office website said: “The situation in Turkey appears to be calming following an attempted coup overnight on 15-16 July. The security environment, however, remains potentially volatile.
“Following earlier disruption, flights to and from airports in Turkey are returning to normal, although some disruption remains and you should check with your airline or tour operator before travelling. You may need to turn up at the airport earlier than normal to get through the additional security checks in place.
“If you are in Turkey, please follow the advice of the authorities, closely monitor travel advice and contact your airline or tour operator.
“In Ankara and Istanbul we advise you to avoid public places, in particular demonstrations, and remain vigilant. Take sensible precautions if you are in the vicinity of any military or security forces. Roadblocks are in place in some areas.
“The coastal resorts do not appear to be significantly affected at present. You should check with your airline or tour operator before travelling to the airport. Continue to exercise vigilance in resort areas.”
The UK’s largest travel association, Abta, said the situation remains “fluid”, adding: “Abta recommends that members of the public read and follow the Foreign & Commonwealth Office (FCO) advice and any advice or instructions issued by their travel provider or airline. There has been no change to FCO advice regarding travel to Turkey and holiday programmes to the resort areas continue to operate.
“The vast majority of British travellers to Turkey will fly directly to the beach resorts on Turkey’s south coast which are hundred of miles away from Istanbul and the capital Ankara.”
Abta estimates that there are currently 50,000 people on holiday with its members in Turkey, while the Foreign Office said more than 2.5 million British nationals visit Turkey every year.
But the tourism industry in Turkey has taken a hit due to recent terror attacks and the country’s proximity to Syria.