The official told Reuters the two men, who entered Turkey from Syria, were thought to have been preparing an attack on Kizilay square in the center of Ankara, where crowds usually gather to celebrate the New Year.
A spokesman for the police terrorism division in Ankara declined to comment.
A double suicide bombing blamed on Islamic State killed more than 100 people in Ankara in October, and Turkey has since stepped up its efforts to tackle the militants.
Turkey has a 900-km (550-mile) border with Syria, some of which is controlled by Islamic State on the Syrian side and has been used as a transit route by would-be jihadists from early on in Syria's civil war.
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