Iraqi Kurdish president Masoud Barzani on Tuesday blamed the loss of Kirkuk on internal disputes between Kurdish politicians.
The surrender by Kurdish forces in the northern city on Monday has highlighted divisions between the two main Kurdish political parties, Mr Barzani's Kurdish Democratic Party (KDP) and the party of his late rival Jalal Talabani, the Patriotic Union of Kurdistan (Puk), with each accusing the other of "betrayal".
Mr Barzani said "the withdrawal of Kurdish Peshmerga troops in Kirkuk was [the] result of a political party's unilateral decision", referring to the Puk.
On Monday, Iraqi prime minister Haidar Al Abadi ordered his troops to raise their flag over all Kurdish-held territory outside of Iraq's autonomous Kurdish region. They achieved a swift victory in Kirkuk, reaching the centre of the city the very same day. The government's gains shifted the balance of power in the country almost overnight.
Mr Barzani pledged that the objective of the Kurdish leadership was to “defend the rights of the people of Kurdistan”.
“We have always tried to get our rights through peaceful means,” he said. “Our objective is to defend the rights of the people of Kurdistan and to provide security for them.”
Also on Tuesday, Iraqi president Fuad Masum blamed last month's Kurdish independence referendum for the government's decision to send troops to take control of Kirkuk city and other parts of oil-rich Kirkuk province.
"Holding a referendum on the Kurdistan region's independence from Iraq stirred grave disagreements between the central government and the government of Kurdistan," said Mr Masum, who is himself a Kurd.
The vote "led to federal security forces retaking direct control of Kirkuk", he said.
Iraqi vice president Ayad Allawi meanwhile called for unity and for the conflict between Baghdad and the Kurdish region to be resolved "peacefully".
On the ground on Tuesday, Kurdish troops pulled out of the long-disputed Khanaqin area near the Iranian border while Iraqi government forces took control of the two largest oilfields near Kirkuk city. Elsewhere, a Yazidi group allied to Baghdad took control of the town of Sinjar.
The Iraqi government's military operation has redrawn the map of northern Iraq, rolling back gains made by the Kurds in recent years.
It comes after the September 25 referendum on Kurdish independence, which was declared illegitimate by Iraq's central government. Voters in the Kurdish autonomous region and Kurdish-held areas elsewhere overwhelmingly backed secession.
In Kirkuk, one of Iraq's most diverse cities, members of the Turkmen ethnic group who opposed Kurdish rule celebrated its recapture by Baghdad on Monday, driving through the streets and firing weapons in the air.
By Tuesday, the once ubiquitous green, red and white Kurdish flag with a blazing yellow sun had vanished from the streets. US-trained Iraqi special forces and local police patrolled to maintain order. Markets, shops and schools were open as normal.
"Life has gone back to normal today, I was able to send my children to school and my husband returned to work today. We are relieved to see Iraqi forces on the streets of Kirkuk," said Asil Olgu, a teacher living in Kirkuk who is of Turkmen origin.
Some Kurdish families who left the city on Monday were already returning home. They said thousands of Kurdish fighters in convoys had formed a long queue as they tried to flee Kirkuk for Erbil, the capital of Iraqi Kurdistan, clogging the road and making it difficult for civilians to leave.