It said the troops had reached the villages of Khaya Rash, Bunwaq, Janarouq and Kelirosh.
"The troops are now based there," the channel said.
Tension between Iraq and Turkey has been high since October 21 when the Kurdistan Workers' Party (PKK) ambushed a Turkish military patrol, killing 12 soldiers.
Since then Ankara has been threatening to launch a military incursion into Iraq to flush out PKK fighters hiding out in the mountainous north.
But lobbying by the United States and appeals by Baghdad stopped them from staging a full-fledged incursion.