US Defense Secretary Jim Mattis said Friday that Washington is working to reduce tensions between Iraqi federal and Kurdish forces, urging them to remain focused on the war against jihadists.

"We are trying to tone everything down and to figure out how we go forward without losing sight of the enemy, and at the same time recognizing that we have got to find a way to move forward," he told reporters.

"Everybody stay focused on defeating ISIS. We can't turn on each other right now. We don't want to go to a shooting situation," he added, using an alternative name for the Islamic State (IS) jihadist group.

Iraqi forces on Friday retook positions in the oil-rich province of Kirkuk that had been controlled by Kurdish peshmerga fighters since 2014, amid a bitter row with the Kurds over a referendum on independence held last month.

A senior Kurdish official said thousands of heavily-armed fighters were deployed around the city of Kirkuk and had been ordered to defend it "at any cost."

Iraq's autonomous Kurdish region gained or solidified control over northern territory including Kirkuk that is claimed by both it and Baghdad after federal forces fled during a devastating IS offensive in June 2014.

Baghdad is bitterly opposed to Kurdish ambitions to incorporate the oil-rich province in its autonomous region.

Iraqi federal forces and the peshmerga have both been key allies of the US-led coalition in its fight against IS.

But with large-scale operations against IS in Iraq moving closer to their conclusion, political disputes that were overshadowed by the war against the jihadists are increasingly returning to the fore.