Prime Minister Nuri al Maliki, meanwhile, broadened an amnesty offer aimed at undercutting support for militants who last month conquered Iraq's second city and large swathes of land which the US top general warned government forces would need help to retake.
Iraqi Kurdish president Massud Barzani told the autonomous region's parliament it should make "preparations to begin to organise a referendum on the right of self-determination".
"It will strengthen our position and will be a powerful weapon in our hands," he said.
The prospect of an independent state is made more attractive by what the Kurds say is Baghdad's unwillingness to resolve the issue of disputed territory and late and insufficient budget payments to the region.
Barzani said Kurdish forces would not pull out from northern territory they occupied after federal forces withdrew at the beginning of the mlitant offensive, giving them control of areas they want to absorb over Baghdad's strong objections.
Maliki on Wednesday said "no one has the right to exploit the events that took place to impose a fait accompli" and that the Kurds' steps towards self-determination were unconstitutional.
On the ground, Iraqi forces were struggling to break the stalemate.
Security forces entered Awja, executed dictator Saddam Hussain's birthplace, after fierce clashes but the government had yet to reclaim the nearby city of Tikrit despite a more than week-long offensive.
The top provincial official has said soldiers were advancing slowly because of booby traps and bombs planted along roads.
West of the northern city of Kirkuk, a roadside bomb killed one Kurdish peshmerga fighter Thursday and wounded four others.
The cost of the conflict has been high for Iraq's forces. Nearly 900 security personnel were among 2,400 people killed in June, the highest figure in years, according to the United Nations.
Meanwhile, Washington has contacted Iraqi players and widened efforts to convince key regional leaders to help resolve Iraq's political chaos.
President Barack Obama called Saudi Arabia's King Abdullah and Vice President Joe Biden spoke to former parliament speaker Osama al Nujaifi, a prominent Sunni.
The White House gave the Kurdish leader's idea for an independence referendum a cool reception.
"The fact is that we continue to believe that Iraq is stronger if it is united," said White House spokesperson Josh Earnest.
"That is why the United States continues to support an Iraq that is democratic, pluralistic and unified, and we are going to continue to urge all parties in Iraq to continue working together toward that objective."
Biden later met Barzani's chief of staff Fuad Hussein at the White House, and told the Kurdish delegation of the "importance of forming a new government in Iraq that will pull together all communities" to combat the Islamic State (IS) a White House statement said.
He also spoke about Iraq's plight in a telephone call with Turkish Prime Minister Recep Tayyip Erdogan.
US Secretary of State John Kerry phoned Barzani, stressing the important role the Kurds could play in a new unity government in Baghdad. That is seen as vital to meeting the challenge of Islamic State militants leading the militant offensive.
The top UN envoy in Iraq, Nickolay Mladenov, told AFP the country faced a crisis akin to the devastating Syria conflict if politicians allowed a total institutional collapse.
"If Iraq does not follow its constitutional political process, what is the alternative? It risks descending into a Syria-like chaos. And that is what people really need to understand, very very quickly," he said.
Mladenov said a lot of damage had been done during the militant offensive that took second city Mosul before the IS declared a pan-Islamic state on a vast territory straddling Iraq and Syria.
"Iraq will never be the same as before Mosul," he said.
Speaking to reporters in Washington, General Martin Dempsey - chairman of the US Joint Chiefs of Staff and an Iraq veteran - argued government forces would need help.
"If you are asking me will the Iraqis, at some point, be able to go back on the offensive to recapture the part of Iraq that they've lost... probably not by themselves," he said.
But he added this did not necessarily mean the United States would have to take military action.
"I'm not suggesting that that's the direction this is headed," Dempsey said.
On Tuesday, Iraq's Council of Representatives met for the first time since its election in April, but MPs failed to elect a speaker, with some trading threats and others walking out.
The legislature is due to reconvene on Tuesday. Once they agree on a speaker, they then have to select a president and a government.
Maliki's Wednesday amnesty offer appeared aimed at splitting the broad alliance of militants, Saddam loyalists and anti-government tribes waging the offensive.
He made the offer to "all tribes and all people who were involved in actions against the state" but who now "return to their senses", but excluded those involved in killings.
He later added former officers from Saddam's armed forces to the amnesty offer.
COMMENTS (3)
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There is urgent need for India, Pakistan and Afghanistan (may include Iran and China also) to work together and eliminate all islamic terrorists, be they TTP, Afghan taliban or anyone else. Keeping these terrorists in their countries by both Afghanistan and Pakistan is an invitation to the forces like ISIS. Pakistan should take off its blinkers, forget Kashmir and Siachen if it wants Durand Line not to be altered and keep Baluchistan. Reports say that there is $1 trillion mineral wealth in Afghanistan. It could be the same or even more lying in Baluchistan. If all countries start to work peacefully for everyone's economic prosperity, it would change the region.
Another Islamic state fails .