A Kurdish official said its forces had successfully beaten back an attack in the region of Rabi'a, 40 kilometres (25 miles) south of the strategic Fish-Khabur border crossing and oil export pipeline hub.

An Iraqi military spokesman denied there had been any clashes in the area, but an Iraqi security source in Baghdad and a rights activist in northwest Iraq said the confrontation had started at dawn on Tuesday, Reuters reported.

So far Baghdad government assaults have targeted disputed Kurdish territory, but Fish-Khabur is firmly within the autonomous Kurdish region, meaning an attack there would signify a major escalation.

"Peshmerga repelled the attack and pushed Popular Mobilisation back in to Rabi'a," tweeted KRG President Massoud Barzani's media adviser, Hemin Hawrami. A military spokesman in Baghdad said in response: "There are no clashes."

Fish-Khabur is strategically vital because oil from both Kurdish and government-held parts of northern Iraq cross at a pipeline there into Turkey, the main route for international export, and therefore a crucial income source for an independent Kurdistan.

The crossing has been under effective Kurdish control since 1991 when the US imposed a no-fly zone over northern Iraq to protect the Kurds from Saddam Hussein's army.

In the wake of Kurdistan's independence vote, Iraqi forces and allied militias last week took control of the northern Kirkuk province and its lucrative oil fields, together with Nineveh and Diyala, territory that the Kurds had captured from the Islamic State group.

Iraqi federal and paramilitary forces on Sunday said they lost five men in the week-long clashes with Kurdish fighters, bringing the death toll for all sides to 31.

US Secretary of State Rex Tillerson visited Baghdad on Monday, but Abadi dismissed his call for Iraq to reject the role of Iran-backed Shia paramilitaries that fight alongside government troops and have taken a hard line on the Kurds.