Iraq's lightning seizure of oil-rich Kirkuk has pitched the country's main Kurdish factions against each other as Baghdad exploits deep divisions over an independence vote.

Iraqi forces on Tuesday took control of five out of six oil fields in the disputed province, dealing a body blow to Kurdish finances and hopes of establishing a state after the controversial referendum last month.

The advances were the latest in a fast-paced operation over the past few days that has seen central authorities reclaim the key territory as Kurdish forces retreated with little resistance.

Behind the sudden Kurdish withdrawal was the historic rivalry between the Kurdistan Democratic Party (PDK) of regional president Massud Barzani and the Patriotic Union of Kurdistan (PUK).

The adversaries -- which fought a civil war in the 1990s -- had locked horns over the September 25 poll which saw voters overwhelmingly back splitting from Iraq.

Barzani, who has dominated the autonomous Kurdish region since the US-led 2003 invasion, was the driving force behind the ballot, pushing ahead with it despite Baghdad's fury and condemnation from the US, Turkey and Iran.

Meanwhile the PUK, the party of Iraq's figurehead President Fuad Masum, supported a UN-backed plan for negotiations with Baghdad in exchange for ditching the referendum.

- 'Betrayal' -

In the wake of the referendum, as tensions have soared between the central government and the Kurds, the PDK-PUK feud has also burst to the surface.

When Iraqi forces moved to retake Kirkuk, grabbed by the Kurds in 2014 as the Islamic State group rampaged across the country, fighters loyal to the PUK withdrew.

"Some of our leaders cooperated in the redeployment of the government forces to Kirkuk," a senior party boss in the city told AFP.

"They facilitated their entry without clashes."

The decision, he explained, came as Kurdish authorities refused to arm PUK fighters around Kirkuk despite Baghdad's repeated threats that it would move on the city.

Another official on the front south of Kirkuk insisted that Kurdish forces only pulled back after "a dozen" of their fighters were killed.

The loss of Kirkuk sparked angry recriminations from the PDK-aligned Kurdish peshmerga commanders.

They accused their rivals of "betrayal and aiding a conspiracy" for allegedly siding with the central government.

- 'Barzani's throne' -

Many see the damaging intra-Kurdish spat as the result of pent-up resentment over Barzani's handling of the region.

Critics saw the referendum gambit as a way to shore up his grip over Kurdistan and its lucrative oil revenues in the face of bitter opposition.

"While we were occupied with protecting the Kurdish people, Massud Barzani was hustling to steal petrol and reinforce his influence," said Lahour Sheikh Zengi, the head of counter-terrorism in the PUK stronghold of Sulaimaniyah.

"From now on we are not going to sacrifice our sons for the sake of Barzani's throne."

PUK lawmaker Ala Talabani said that "no one knows" what had happened to the money from oil wells that Barzani has controlled since 2014.

The Kurdish leader's recent moves have fuelled suspicions that he is looking to further extend his rule.

Barzani, who has lingered in power for years without a clear mandate after parliament extended his tenure in 2013, had bowed to pressure and decided not to run in elections next month.

But the crisis over the referendum has thrown that ballot into doubt and Barzani has set up a new "leadership" body -- headed by himself.

While the political future of Kurdistan is mired in uncertainty, one thing does seem increasingly clear.

The internecine squabbles appear to have buried for now any hope of Kurdish independence. The regional government's coffers will be gutted without the oil revenue it once received from Kirkuk.

"With the loss of these fields, Kurdish finances have been cut in half," French geographer and regional specialist Cyril Roussel told AFP.

"It spells the end of Kurdistan's economic self-sufficiency and of the dream of independence."