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One name that has surfaced repeatedly in recent days is Ahmad Chalabi, who led the lobbying for the 2003 U.S. military invasion of Iraq and who was an early favorite of President George W. Bush to succeed the ousted Saddam Hussein.

Mr. Chalabi fell out of favor in Washington when it was found that he fed U.S. officials faulty intelligence about Iraq’s weapons of mass destruction programs, but his Iraqi National Congress party has remained a factor in Iraqi politics.

Although the party now holds just one seat in Iraq’s parliament, news reports say Mr. Chalabi, a self-proclaimed secular Shiite, is a potential player whom Iraqi Sunnis, Kurds and Shiites might agree on to replace Mr. al-Maliki.

U.S. efforts

In Washington, White House spokesman Josh Earnest said Wednesday that the initial failure of Iraq’s parliament to choose new leaders this week was “an indication that that process is not off to a good start.”

Mr. Earnest said the Obama administration is holding out hope for the quick formation of a new government that can tackle the rising threat posed by the Sunni extremists. He also said Vice President Joseph R. Biden had phoned Osama al-Nujaifi, a Sunni who previously served as the speaker of Iraq’s parliament.

Mr. Biden is “talking to people who might have some influence over the ability of Iraq’s political leaders to come together and make the formation of an inclusive government a priority,” Mr. Earnest said.

President Obama, meanwhile, called King Abdullah of Saudi Arabia to discuss the Iraq crisis. Mr. Obama also thanked the king for Saudi Arabia’s pledge of $500 million in aid to Iraqis who have been displaced by the violence.

Tens of thousands have sought refuge in the relative calm of Kurdistan in northern Iraq, according to the Kurdish envoys.

Kurdistan fought for autonomy from Baghdad when Saddam was in power, but territorial boundaries remain uncertain.

Kurdish minorities can be found in Turkey, Syria and Iran, all of which have aggressively opposed the idea of an independent Kurdish state.

“At the end of the day, even if we go down the road to independence, we want international recognition,” Mr. Bakir said.

“We do understand that without the support of the neighboring countries, or at least some of them, without the support of some of the main powers in the world, the United States included, we cannot have it survive,” Mr. Bakir said.

Dave Boyer contributed to this report.