Iraqi government and Kurdish forces have clashed in the contested city of Kirkuk

Both have been equipped and trained by the U.S. to fight against ISIS in Mosul

The escalation comes following last month's contentious independence referendum

Many Kurds in Kirkuk are angry at their own troops for retreating, while Arab residents have welcomed the arrival of the army

The Iraqi city of Kirkuk is the scene of fighting Monday morning, as government soldiers clash with Kurdish troops.

Despite years of pursuing the same goal against ISIS in Mosul and its surroundings, the two US-trained and equipped fighting forces have turned on each other.

Iraq’s Prime Minister Haider al-Abadi had ordered the army, and affiliated militias, to “impose security” on the disputed city following the recent referendum on Kurdish independence.

Kirkuk, claimed by both Baghdad and Irbil, is not part of the autonomous Kurdistan region, despite having a Kurdish majority. The city also has considerable Arab and Turkmen populations, and boasts considerable oil reserves.

It is the oil fields, along with some military bases, that Abadi’s government seeks to retake from the Kurdish forces who have controlled them since the ISIS takeover in 2014.

A tweet from the Kurdistan Region Security Council indicated that Iraqi forces had launched a “major, multi-pronged operation intended to enter the city and take over K1 base and oil fields” late on Sunday.

STATEMENT: Iraqi forces/PMF attacked Peshmerga forces in South Kirkuk in operation using US equipment, incl. Abrams tanks. #SupportKurdistan pic.twitter.com/C95Qfrb77y — KR Security Council (@KRSCPress) October 16, 2017

Arabic-language Iraqi news pages on social media quoted the Iraqi “War Media Cell” as saying that the K1 base had been completely recaptured on Monday morning.

It was also reported that a number of sites had been retaken by central government, including bridges, roads and the industrial zone to the south, as well as a power station. Kurdish authorities confirmed that the south of the city is in Iraqi control.

The Arabic-language page “Kirkuk is my town” suggested that there was no power in the city, and that schools had been closed.

While Iraqi government troops are backed by the U.S., which led coalition efforts in Mosul, Kurdish authorities have expressed concern about claims that Iran-backed Hashd al-Shaabi militias are using American equipment to battle Kurds.

Footage today shows Iranian-backed PMF deployed near Maktab Khalid, SW of Kirkuk, using US equipment for attack on Kirkuk. #SupportKurdistan pic.twitter.com/bajU2YPvzp — KR Security Council (@KRSCPress) October 16, 2017

Peshmerga forces attacked by Iraqi forces/PMF in #Kirkuk using US equipment, incl Abrams tanks & Humvees gifted to Iraq for the war on Isis. pic.twitter.com/Mqzw7FGofb — KR Security Council (@KRSCPress) October 16, 2017

The Popular Mobilization Forces (PMU) as they are known in English were made an official part of Iraq’s armed forces in December 2016, but many elements of the umbrella organization continue to be directly funded by Iran.

The U.S. Defense Department itself has urged both sides “to avoid additional escalatory actions” which could undermine efforts against ISIS.

There have also been suggestions that Iraqi Kurdish Peshmerga fighters have been joined by members of the Kurdistan Workers Party (PKK), which has carried out a campaign of attacks on Turkey. Iraq's parliament has previously warned that such a move would be taken as a declaration of war.

BBC news correspondent Orla Guerin tweeted this image of possible foreign PKK troops in Kirkuk.

Peshmerga fighters from outside #Kirkuk who have come to help defend the city - possibly PKK from Turkey. pic.twitter.com/w7R2HaIDf0 — Orla Guerin (@OrlaGuerin) October 16, 2017

Anger is running high in Kirkuk, with footage of Kurdish residents apparently throwing stones at withdrawing Peshmerga troops circulating on social media.

Jenan Moussa, reporter for Dubai-based Akhbar Al Aan, who is on the ground in Kirkuk, tweeted that many Kurds are angry at their own forces over the advance of Iraqi troops.

12- I can't describe how angry people are on Kirkuk streets. There is disappointment that some PUK Peshmergas withdrew without fighting. — Jenan Moussa (@jenanmoussa) October 16, 2017

In an indication of the divide between Kurdish and non-Kurdish civilians in the city, pictures of locals seeming to welcome Iraqi government troops were also widely shared.

People in #Kirkuk welcome Iraqi security forces with tea and sweets. pic.twitter.com/RJ6L13OEoG — Ihsan (@Thawra_city) October 15, 2017

The escalation follows a series of moves against the Kurdistan Regional Government by central government, after Iraqi Kurds last month voted overwhelmingly in favor of independence in a poll rejected as "unconstitutional" by Baghdad.

Soon afterwards, international flights were suspended from Irbil and Sulaymaniyah airports, and Iraq joined Turkey in conducting military exercises on the border.

Crisis talks between the two sides broke down on Sunday.