Turkey’s military, which rarely talks to the media, could not immediately be reached to confirm the reports.
Broadcaster NTV said Turkish commandos had gone up to 5 km (3 miles) into Iraq to target camps belonging to Kurdistan Workers Party (PKK) militants. It said the offensive, which followed a Turkish air operation in the area, was finished.
Turkey’s parliament last month extended by a year a mandate allowing the government to send troops into northern Iraq in pursuit of PKK fighters, despite objections from Baghdad.
The mandate was first passed in 2007 and has been extended every year since, permitting the army to enter Iraq to strike the PKK, which is designated a terrorist group by Ankara, the United States and the European Union.
Turkey most recently sent ground forces into Iraq in 2008 and has an estimated 1,000 troops based there under an agreement with Iraq dating from the 1990s.
Officials from the central government in Baghdad, as well as officials from the Kurdistan Regional Government (KRG) in the north, did not immediately answer calls seeking confirmation of the Turkish military operation.
The past few months have seen some of the heaviest fighting between Turkish forces and the PKK since the militants took up arms in 1984, with Turkish fighter jets and attack helicopters bombarding the rebels on both sides of the Iraqi border.
Relations between Turkey and Iraq have cooled sharply in recent months over mutual charges of sectarianism, and Baghdad last month asked Turkey to stop attacking the PKK on its territory.
More than 40,000 people, mainly Kurds, have been killed in almost three decades of violence since the PKK began fighting to try to carve out a separate state.
In a separate motion, Turkey’s parliament last month also authorized the government to send troops into Syria, Turkey's southern neighbor, in response to shelling by President Bashar al-Assad’s forces of Turkish territory that had killed civilians.
Prime Minister Tayyip Erdogan, a vocal critic of Assad’s crackdown on a popular uprising, has accused Syria’s government of backing the PKK in its recent escalation of attacks.