161 people lost their lives after an attempted coup by a military faction on Friday night.
A flight to Dalaman in the south-west of the country left Aldergrove on Saturday afternoon.
Tour operator Thompson said most travellers had decided to continue with their holiday plans.
Sharon Laverty and her friend Victoria Hewer told the BBC that they were reassured by the fact the flight was still operating.
A male holiday maker said: "No difference to Belfast over the last 40 years, so why spoil the holiday?"
Another traveller, Brian McCullough, said: "Where we are going is hundreds of miles away from the trouble in Ankara and Istanbul, so it shouldn't be a problem."
Dylan McKee is a regular visitor to Turkey.
He said he had no concerns: "We know people out there and they are telling us it is safe, so we'll go out there, we'll have our holiday and we'll come home, we'll be safe."
The Foreign Office issued updated advice to travellers on Saturday: "We strongly advise you to stay indoors, avoid public places, in particular demonstrations, and remain vigilant.
"Avoid areas of conflict and take sensible precautions if you are in the vicinity of any military or security forces."
The latest advice from the Irish government is for "Irish citizens in Turkey or intending to travel to Turkey is to exercise a high degree of caution."
"The situation in Ankara and Istanbul in particular remains tense, and there is a heightened security presence on the streets in both cities.
"There have been incidents of violence, and Irish citizens should be extremely vigilant and stay informed of local developments and security advice.
Despite political turmoil, most holiday makers bound for Turkey left Belfast International Airport unfazed on Saturday.