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Failure to achieve a similar agreement with Baghdad forced Washington to withdraw all U.S. combat troops from Iraq in December 2011.

In Kabul, Mr. Karzai said Monday that a national assembly of elders, known as a loya jirga, must decide on the U.S. demand for immunity for its troops, not his administration.

“It is the decision of the people of Afghanistan. So a loya jirga of the people of Afghanistan should decide,” Mr. Karzai said, according to The Associated Press.

Some Afghan lawmakers are inclined to support a conditional presence of U.S. troops after 2014.

“The Afghan people will let American troops stay beyond 2014 so long as they don’t interfere in Afghanistan’s sovereignty,” Mrs. Zaki said. “It is good to have American troops in Afghanistan because the people believe that, after 2014, the Taliban will come back and they will be in danger.”

Afghan women in particular are worried that the gains they have made over the past decade will be erased if the Taliban returns to power.

At a joint news conference with Mr. Karzai in Washington on Friday, Mr. Obama said U.S. forces will play only a supporting role in Afghan security, beginning this spring. This will accelerate the transition, which had been set to start by the middle of the year.