Turkey on Monday said it has launched an air and ground offensive against militants of the outlawed Kurdistan Workers' Party (PKK) in northern Iraq.

Iraq handed Turkish ambassador Ali Riza Guney a "firmly-worded note of protest" urging its northern neighbour to "put an end to acts of provocation and unacceptable violations", the foreign ministry said in a statement.

Designated as a terrorist group by Ankara and its Western allies, the PKK has been waging an insurgency against the Turkish state since 1984 that has claimed tens of thousands of lives.

Turkey routinely carries out attacks in northern Iraq, where the PKK has bases and training camps in the Sinjar region and on the mountainous border with Turkey.

"The Iraqi government renews its call for the withdrawal of all Turkish forces from Iraqi territories in a manner that reflects binding respect for national sovereignty," the Iraqi statement said.

Iraqi President Barham Saleh, himself a Kurd, on Tuesday condemned the Turkish offensive as a "violation of Iraqi sovereignty and a threat to national security".

The repeated Turkish operations have tested relations between Baghdad and Ankara, key trade partners.

They also complicate ties with the regional government in Iraqi Kurdistan, which has an uneasy relationship with the PKK.

The latest offensive comes two days after a visit to Ankara by the Kurdistan region's prime minister, Masrour Barzani.