France's Macron invites Iraq PM to Paris to discuss Kurdish vote

French President Emmanuel Macron has invited Iraqi Prime Minister Haider al-Abadi to visit Paris on Thursday, saying the aim is to calm tensions after the deeply divisive Kurdish independence referendum.

In a statement, the presidency said France wanted to "help Iraq to stop tensions from setting in" following the vote on Monday, which saw Iraqi Kurdistan overwhelmingly support secession.

In a phone call on Wednesday, "Macron stressed the importance of preserving the unity and integrity of Iraq while recognising the rights of the Kurdish people. Any escalation must be avoided," the presidency said in the statement late on Friday.

"Faced with the priority of fighting Daesh and the stabilisation of Iraq, Iraqis must remain united," it added, referring to the Islamic State group.

The office of Abadi, however, on Saturday denied that Macron's invitation had any link to the crisis with Iraqi Kurdistan.

"There is no relation between the invitation and the crisis caused by the unconstitutional referendum," it said.

"The visit aims to reinforce bilateral relations and to focus on the fight against terrorism in the region in which Iraq has achieved enormous victories," it added.

Iraqi forces ousted IS from the northern Nineveh province on August 31, and is now fighting to retake the jihadist group's last footholds in the country.

Abadi's office stressed the invitation was first made when French Foreign Minister Jean-Yves Le Drian and Defence Minister Florence Parly visited Baghdad on August 26.

It said Macron had made no mention of "the need to recognise the rights of the Kurds or stopping an escalation by Baghdad".

"On the contrary, there was a condemnation of the insistence of the Kurdish leadership to hold this referendum and expose the region to instability".

While Monday's independence vote was non-binding, it has nonetheless sent tensions in the country and the region soaring.

In response to the poll, the Iraqi government has cut Kurdistan's direct air links with the outside world, partially isolating the northern region.

Turkey and Iran, which both have their own Kurdish minorities, have denounced the referendum, while the United States described it as "unilateral" and lacking legitimacy.