The FCO had warned on the weekend that Brits in the country should stay inside after a section of the military tried to overthrow the government on Friday.
However, the FCO has said the situation “appears to be calming”. It adds that the security environment “remains potentially volatile” and Brits should avoid public places in Ankara and Istanbul.
Abta said some 50,000 British tourists were understood to be on holiday in Turkey.
Flights are now returning to normal, but travellers are being urged to check with their airlines or tour operators before travelling.
Brits in Turkey have been told to follow the advice of the authorities and closely monitor travel advice.
The FCO added: “Apart from Marmaris, 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.”
Meanwhile, Turkish Airlines is offering passengers who have booked on the Turkish Airlines and AnadoluJet flights from and to Turkey the chance to refund or rebook tickets, subject to terms and conditions.
FCO relaxes Turkey advice but caution still urged for Brits
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