The Maroon Berets, part of a specially trained anti-terrorist force, moved about 3 miles from the border, Today's Zaman reported. They were returned to Turkey by air.
The newspaper said no information was available about any casualties.
Since 1984, about 50,000 of people have been killed in clashes between the Turkish military and the Kurdistan Workers Party, usually known by its Turkish acronym PKK.
Last month, the Turkish Parliament extended authorization for cross-border operations in Iraq by a year.
Notable deaths of 2014 [PHOTOS]