Both the Islamic State group (IS) and Kurdish militants have claimed a number of attacks in Turkey in recent months.
Turkey is part of the US-led coalition against IS, and coalition planes use its air base at Incirlik for raids in Iraq and Syria.
Turkey is also conducting a campaign against Kurdish militants.
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A ceasefire between the government and the Kurdistan Workers Party (PKK) broke down last year.
On Saturday an emergency travel warning was published on the website of the US embassy in Turkey.
"There are credible threats to tourist areas, in particular to public squares and docks in Istanbul and Antalya. Please exercise extreme caution if you are in the vicinity of such areas," it read.
Antalya, on Turkey's Mediterranean coast, is a major tourist centre visited by millions of people every year.
The warning comes a day after Israel's counterterrorism bureau urged all Israelis to avoid Turkey, saying: "There are immediate risks of attacks being carried out in the country, and we stress the threat applies to all tourism sites in Turkey."
The US has warned its citizens of "credible threats" to tourist areas in Turkey, particularly in Istanbul and the southern resort city of Antalya.