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“We continue to encourage all the parties to form an inclusive government that reflects the will of the voters, involves significant power-sharing among the major blocs, and will guide Iraq through its next chapter,” the official said.

Mr. Talabani, however, said the pressure on his father to resign was reigniting old fears for many Iraqis.

“The Kurds have been the strongest ally and partner of the United States since before the liberation and certainly during it,” he said. “And for the United States to be leaning on us, as they are now, in effect handpicking the new leaders of Iraq, is not respectful of Iraq’s parliamentary system and touches on all of the insecurities of the Kurds, that the United States will once again betray us.”

Kurds consider the first U.S. betrayal to have occurred in 1975, when the U.S. and the Shah of Iran agreed to end all support for the Kurdish rebellion in Iraq in exchange for Iraqi concessions on water rights over the Shatt al Arab waterway between Iraq and Iran.

In 1988, then-Iraqi President Saddam Hussein began the Anfal campaign to depopulate the northern Iraqi Kurdish regions, a military campaign that included the use of nerve gas on Kurdish civilians in the town of Halabja. The U.S. during this period sold Iraq grain credits and only made a symbolic protest.

At the close of the 1991 Persian Gulf War, President George H.W. Bush gave a speech urging Iraqis to rise up against Saddam, but privately the U.S. allowed him to use attack helicopters to put down the rebellion even though the U.S. and its coalition partners controlled Iraq’s air space.

According to U.S. and Iraqi officials, Mr. Biden in a phone call last week offered the Kurds the speakership of the Parliament and the Oil Ministry and also a public statement offering the Kurds a security guarantee.

Mr. Biden’s office declined to comment for this report.

On Tuesday, Republican Sens. Lindsey Graham of South Carolina and John McCain of Arizona, and Sen. Joe Lieberman, Connecticut independent, urged Massoud Barzani, president of the Kurdistan region, to replace Mr. Talabani as well.

Reidar Visser, a researcher at the Norwegian Institute of International Affairs and proprietor of the Gulf Analysis blog, said: “I find this strange that the Obama administration is pushing so hard for Iraqiya to get the presidency, because the speakership will be more powerful.”

Mr. Visser added that the veto powers of the president will expire this year.

“The Americans do not appreciate the challenges involved in upgrading the presidency to the level where it has power that would make it attractive to Allawi,” he said. “That will require constitutional change, and that would require a referendum. So it’s hard to see how the Americans can make good on their promise.”