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“Hopefully it’ll be certified and it’ll be seen as legitimate,” Mr. Jones told CNN.

“This is the first election that the Afghans have run themselves and so it’s probably destined to be a little bit imperfect. … But the important thing is that the Afghan people feel that President Karzai is their legitimate president. … It is very important that they support the legitimately elected president,” he added.

Ms. Fair noted that it would be impossible to hold a runoff vote until the spring because of cold weather and the time it would take to print new ballots. That would leave Afghanistan with uncertainty at the top at a time when the U.S. needs a coherent government to defeat a spreading Taliban insurgency.

Mr. Karzai’s administration had been marred by allegations of corruption and poor administration even before the vote.

The situation has been further roiled by the firing of a top U.N. official from his post in Afghanistan last week. Peter Galbraith, who served as the deputy special representative of the United Nations in Afghanistan, said as many as 30 percent of Mr. Karzai’s votes are fake.

Two other candidates, Mr. Abdullah and Ramazan Bashardost, a former planning minister, also benefited from reported vote rigging but to a much lesser degree, Mr. Galbraith told The Times in an e-mail.

Preliminary but possibly tainted results gave Mr. Karzai nearly 55 percent of the vote and Mr. Abdullah 28 percent.

Afghanistan’s Independent Election Commission and the U.N.-supported Afghan Electoral Complaints Commission (ECC) are in the process of auditing selected suspect ballots. Election observers, including Mr. Galbraith, predicted that the exercise would confirm significant fraud.

However, Ms. Fair said, “the fact that the international community blessed Karzai even before the election has been certified significantly undercuts the election commission’s role.”

Mr. Galbraith said he was fired for insisting that the United Nations Assistance Mission in Afghanistan investigate “ghost” polling stations that produced thousands of fraudulent votes. He said his boss, Norwegian diplomat Kai Eide, “lobbied hard for my removal.”

“Galbraith was treated unfairly,” said Ms. Fair. “He was arguing for the most principled position: Back the process, not the person.”

U.N. Secretary-General Ban Ki-moon’s spokeswoman, Michele Montas, said earlier this week that Mr. Ban had “total confidence” in Mr. Eide.

On Wednesday in a letter to senior U.N. officials, Mr. Eide denied allegations that he downplayed fraud as “nonsense,” the Associated Press reported.

According to a U.N. spreadsheet first reported by The Washington Post, there were large gaps between U.N. estimates of turnout and Afghan tallies of votes in the south and east of the country where ethnic Pashtuns predominate. Mr. Karzai is a Pashtun.

“This is a total mess,” said Jamie F. Metzl, executive vice president of the Asia Society, who also served as an election monitor. “The elections themselves were structurally flawed, as all of the major observer groups noted … The U.N. should do much more.”

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