BAGHDAD: The US-led coalition battling Daesh urged Baghdad and Iraq's Kurds on Monday to "avoid escalatory actions" after Iraqi forces launched an operation to retake parts of Kirkuk province.

"We continue to advocate dialogue between Iraqi and Kurdish authorities. All parties must remain focused on the defeat of our common enemy, ISIS, in Iraq," Major General Robert White, a commanding general in the coalition, said in a statement.

The Iraqi operation, which follows weeks of soaring tensions between two US allies in the battle against Daesh, aims to retake oil and military sites in Kirkuk that Kurdish forces took over during the fightback against the militants.

It follows the referendum last month which saw Iraqi Kurds overwhelmingly back independence for their northern region, despite warnings from Washington that the vote would complicate efforts to tackle the militants.

At least 10 Kurdish fighters were killed and 27 wounded during fighting overnight with Iraqi pro-government paramilitary forces, a Kurdish official said.

The coalition said it was monitoring movements of military vehicles and personnel in the vicinity of Kirkuk, which is disputed between Baghdad and the Kurds, and denied a wide-scale offensive was under way.

"These movements of military vehicles, so far, have been coordinated movements, not attacks," the statement said.

It said coalition forces were not supporting activities by the Iraqi or Kurdish governments around Kirkuk.

The coalition was aware of reports of clashes, it said. "We believe the engagement this morning was a misunderstanding and not deliberate."