In a rare piece of positive news during the crisis, however, a group of 46 Indian nurses caught up in the conflict were to be freed, one of them said.
Iraqi Kurdish president Massud Barzani told the autonomous region's parliament yesterday that it should make "preparations to begin to organise a referendum on the right of self-determination", but the US opposed the move.
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.
"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."
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US Vice President Joe 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), the group leading the insurgent drive, a White House statement said.
Today, meanwhile, an Indian nurse told AFP that she and 45 colleagues who have been trapped in Iraq by the crisis were to be freed imminently.
The nurses, who were working at a hospital in executed dictator Saddam Hussein's hometown of Tikrit when the militant offensive began last month, are currently being held in the militant-held city of Mosul.
An Indian diplomat, speaking on condition of anonymity, said the group was expected later today in Arbil, which is a short drive from Mosul but has been insulated from the unrest.
The abductions, along with the capture of 39 other Indian workers in Mosul, left Indian authorities scrambling to secure their release and their fate is the first foreign crisis for the new right-wing government of Prime Minister Narendra Modi.
On the ground, Iraqi forces were struggling to break the stalemate.
Security forces entered Awja, Saddam's birthplace, after fierce clashes but the government had yet to reclaim the nearby city of Tikrit despite a more than week-long offensive.