French President Emmanuel Macron has invited Iraqi Prime Minister Haider al-Abadi to visit on October 5 to discuss the Kurdish independence referendum, offering France's help in calming tensions over the vote.

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

"Emmanuel 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 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.

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.