The United States called for Iraqi federal forces to limit their 'movements' in areas claimed by both them and the country's Kurds to avoid more violence between Washington's allies.
Iraqi forces clashed with Kurdish units in the northern province of Kirkuk on Friday, part of a largely bloodless operation that saw them retake swathes of disputed territory from the Kurds in a matter of days.
Both federal and Kurdish forces have been key US allies in the war against the Islamic State group, but a common jihadist enemy did not erase long-running territorial and financial disputes between the two sides.
"In order to avoid any misunderstandings or further clashes, we urge the central government to calm the situation by limiting federal force movements in disputed areas to only those coordinated with the Kurdistan Regional Government," State Department spokeswoman Heather Nauert said in a statement.
As Kurdish authorities have vehemently criticized Iraqi operations in the disputed areas, the statement effectively amounts to a call on them to cease.
The US also urges "all parties to cease all violence and provocative movements, and to coordinate their activities to restore calm," Nauert said.
Iraqi Kurdish forces gained or solidified control over a number of disputed areas in the course of the three-year war against IS, which saw federal troops flee their posts in the north during the initial jihadist onslaught in 2014.
But a non-binding referendum on independence held by the Kurds last month provided the excuse and the winding down of major operations against IS the opportunity for Baghdad to make good its losses.
The US opposed the independence referendum, as did Baghdad and various neighboring states.
But while the US appears likely to have given at least tacit approval to the Iraqi operation, the statement also made clear that federal forces regaining control of disputed territory does not end the debate over the status of these areas.
"The reassertion of federal authority over disputed areas in no way changes their status -- they remain disputed until their status is resolved in accordance with the Iraqi constitution," Nauert said.
Iraq's Joint Operations Command said police, counter-terrorism units and allied militias seized the Altun Kupri region, extending the central government's territory to within 50 kilometres (30 miles) of Arbil, the capital of the autonomous Kurdish region.
The two sides exchanged mortar rounds and automatic gunfire but Iraqi forces managed to "hoist the flag on the municipality building", a security source Kirkuk city said.
A Kurdish general, Ghazi Dolemri, was killed in the fighting, sources said, while an AFP journalist reported further shelling as Iraqi government forces and Hashed al-Shaabi paramilitary forces advanced on Sirawa, five kilometres north of Altun Kupri.
Iraqi forces also said they had retaken the Ain Zalah and Batma oil fields, northwest of Mosul.
Days of gains
The fresh advances came after Iraq's central authorities snatched back control of a swathe of disputed territory from Kurdish forces in a largely bloodless operation launched at the weekend.
The government advances and Kurdish retreat have rewritten the volatile boundaries between the two sides and trashed Arbil's dreams of independence, which soared after a September 25 referendum held in defiance of Baghdad.
The loss of Kirkuk's rich oil fields also dealt a severe blow to the regional government's already parlous finances, heavily dependent on petrochemical exports.
US oil giant Chevron said Friday it had "temporarily" suspended operations in the Kurdish autonomous region.
"We continue to monitor the situation in the Kurdistan Region of Iraq," a spokeswoman said.
"We look forward to resuming our operations as soon as conditions permit."
Iraq's forces have also snatched back areas of Nineveh and Diyala provinces, driving Kurdish forces from positions they seized in the chaos of the Islamic State group's 2014 rampage across northern Iraq and parts of neighbouring Syria.
The agricultural region of Altun Kupri, which means "golden bridge" in Turkish, covers an area of 520 square kilometres (200 square miles) and is mostly inhabited by Kurds and Turkmens.
Security in the Altun Kupri area had been ensured by Kurdish police forces loyal to regional president Massud Barzani ever since the US-led invasion of 2003.
In their bid to halt Iraqi forces, the peshmerga planted explosives that damaged a major bridge linking Kirkuk to their regional capital Arbil over the Little Zab river, according to a local security source.
This week's operation was accelerated by rifts between rival Kurdish factions that saw some forces opposed to Barzani -- the architect of the independence vote -- strike a deal with Baghdad to withdraw.
In Baghdad, Haydar Hamada, a spokesman for Prime Minister Haider al-Abadi, said Iraqi forces were pressing on with the operation to impose government control over the disputed areas.
"We will continue restoring the authority of the federal authorities," he told AFP.
But a peshmerga commander in Arbil accused the Iranian-backed Hashed militia of trying to extend the boundaries of the Kirkuk province into Kurdish territory.
While central government forces have met with little resistance as they pen the peshmerga back into the three provinces that make up the Kurdish autonomous region, sporadic clashes have caused some bloodshed.
Peshmerga commander Wasta Rassoul, a member of the PUK faction that opposes Barzani, said 26 Kurdish fighters had been killed and 67 wounded since Sunday.
Tensions between Kurdish and Iraqi forces have pitted two vital US allies in the fight to destroy the Islamic State group against each other.
The two sides have cooperated in the Washington-backed offensive that has seen the jihadists driven from their major urban strongholds into a rump territory along the border with Syria.