The Kurdish Peshmerga command has said the Iraqi government will pay a "heavy price" for its military campaign in Kirkuk, which it described as "a declaration of war against the nation of Kurdistan".

The warning by the Peshmerga General Command (PGC) on Monday came as Iraqi federal forces, backed by Shia militia, said they had taken full control of oil-rich Kirkuk in a swift advance on Kurdish-held positions.

The PGC accused some of the leaders of the Patriotic Union of Kurdistan (PUK) of "treason", alleging that forces under the party's control had withdrawn from areas they held. The PUK has denied the accusations, according to Kurdish news portal Rudaw.

"Unfortunately, some officials from the ... PUK helped this plot against the Kurdistan nation and committed a great and historic treason against Kurdistan and the martyrs who sacrificed their lives for Kurdistan under the PUK flag," the statement said.

Separately, Hemin Hawrami, special assistant to Masoud Barzani, president of the Kurdish Regional Government (KRG) and leader of the Kurdistan Democratic Party, posted on Twitter what he said was a statement by a main Shia militia group thanking PUK members for their cooperation in helping with the withdrawal from some of the areas around Kirkuk.

'Never united'

Al Jazeera's Charles Stratford, reporting from Erbil, said the fact that Iraqi forces were able to achieve their objective in just about 15 hours has left the KRG shocked and in need for answers.

"Already, there are questions being asked about whether leaders of one of the two main Kurdish political parties colluded with Iraqi military to ensure such a swift and easy victory in and around Kirkuk," he said.

Saad Jawad, professor of political science and senior fellow of the Middle East Centre at the London School of Economics, said "it is a reality" that the Kurdish parties do not often see eye to eye.

"Of course, they agreed on certain things but they were never united," he told Al Jazeera.

"I think the Iraqi government with the pressure of the Iranian government … managed to woo a part of the Peshmerga that belong to the PUK."

'Constitutional duty'

The Iraqi forces' advance was part of a major operation to retake Kirkuk, amid an escalating dispute in the wake of a controversial September 25 referendum on Kurdish secession that Baghdad had declared illegal.

In a rapid push, the Iraqi army seized control of the city's airport, in addition to an oil field, the strategic K1 military base and the Taza Khormatu district southeast of Kirkuk, before capturing the governorate building in the city centre.

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As the Iraqi army advanced, thousands of people, including civilians and Peshmerga fighters, fled the disputed city.

In its statement, the Peshmerga command accused the government of Iraqi Prime Minister Haider al-Abadi of being responsible for initiating "war", warning Baghdad that it will "pay a heavy price for this unfairness".

"We call upon all the real Peshmerga of the country and the resilient and enemy-defeating people to do all they can to resist and defeat the attackers," it said.

For his part, al-Abadi urged the Peshmerga to collaborate in maintaining the peace in Kirkuk.

"We call upon the Peshmerga forces to perform their duty under the federal leadership as part of the Iraqi armed forces," he said in a statement on Facebook, urging "all employees in Kirkuk to continue their work normally and not to disrupt the interests of citizens".

Al-Abadi said he was fulfilling his constitutional duty "to serve the citizens and protect the unity of the country, which was in danger of partition due to the insistence on holding the referendum organised by those in power in the Kurdistan region in a unilateral step".

Kurdish Peshmerga forces took control of oil-rich Kirkuk after the Iraqi army fled from a major offensive by the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group in 2014.

Since then, there has not been an agreement between the KRG and the federal government in Baghdad about who should control the area - and benefit from its vast oil wealth.

Tensions between the two sides have been running especially high since Iraqi Kurds overwhelmingly voted for secession in last month's referendum.

The non-binding poll was held in areas under control of the KRG and in a handful of disputed territories, including Kirkuk.

Shortly after the referendum, the Iraqi parliament had asked al-Abadi to send troops to Kirkuk and regain control of the region's oil fields.