The Turkish leader's comments came a day after Iraq summoned Turkey's ambassador to Baghdad to lodge a formal protest against Erdogan's latest military campaign.

Turkey's armed forces have reported the death of two soldiers and dozens of Kurdish militants since the launch Sunday of their third offensive in northern Iraq since 2020.

Erdogan told a parliamentary meeting of his ruling party that both Baghdad and the leaders of the autonomous Kurdish region based in Arbil supported Turkey's ground and air assault.

"I thank the central government in Iraq and the regional administration for their support to our fight against terror," Erdogan said.

"I wish success for our heroic soldiers involved in this operation, which we are carrying out in close cooperation with the central Iraqi government and the regional administration in northern Iraq."

Officials in Baghdad are publicly voicing displeasure over the Turkish military push into the mountains of northern Iraq, and later on Wednesday the government dismissed Erdogan's claims.

"We promise that everything the Turkish side keeps saying regarding any coordination or agreement with the Iraqi government is not true," foreign ministry spokesman Ahmed Al-Sahhaf said, quoted by state news agency INA.

The ministry for Iraqi Kurdistan's peshmerga fighters on Wednesday also denied any cooperation or participation by Arbil in the Turkish military operation.

"We deny all the accusations and declare that the peshmerga forces did not take part in these operations," it said in a statement, lashing out at "irresponsible media".

The foreign ministry on Tuesday said Iraq handed the Turkish ambassador a "firmly-worded note of protest" urging its northern neighbour to "put an end to acts of provocation and unacceptable violations".

Some analysts believe that Iraqi leaders -- while lodging formal protests -- are privately happy that Turkey is trying to punish fighters from the Kurdistan Workers' Party (PKK).

The group is classified as a terrorist organisation by both 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.