The extra votes add to a list of complaints leveled against the election by the reform candidate, Mir Hussein Moussavi, and other challengers inside and outside Iran. Among them:

How did the government manage to count enough of the 40 million paper ballots to be able to announce results within two hours of the polls closing? How is it that Mr. Ahmadinejad’s margin of victory remained constant throughout the ballot count? Why did the government order polls closed at 10 p.m. when they often stay open until midnight for presidential races? Why were some ballot boxes sealed before candidates’ inspectors could validate they were empty? Why were votes counted centrally, by the Interior Ministry, instead of locally, as in the past? Why did some polling places lock their doors at 6 p.m. after running out of ballots?

Image Opposition supporters rallied on Valley Asr street last week. Credit... The New York Times

In specific terms, analysts who have scrutinized the election results available in Persian and English said that for Mr. Ahmadinejad to have won 63 percent to Mr. Moussavi’s 34 percent, he would have had to have won over most people who four years ago supported the liberal reform candidate, Mehdi Karroubi, a former speaker of the Parliament who ran again this year. They said the president also would have had to have garnered the votes in that 2005 race that went to Ali Akbar Hashemi Rafsanjani, a bitter opponent of Mr. Ahmadinejad who backed Mr. Moussavi this time.

“In the province where Karroubi did best in 2005, his home province of Lorestan, Ahmadinejad got some 71 percent of the vote,” wrote Nate Silver in an analysis that was posted on fivethirtyeight.com, a politics and polling Web site. He added, “If Ahmadinejad won the election, he did it by winning over these rural Karroubi voters. And if he stole it, those were the votes he stole or intimidated.”

The review of voting statistics released this week by St. Andrews University and Chatham House reached a similar conclusion.

“The plausibility of Mr. Ahmadinejad’s claimed victory is called into question by figures that show that in several provinces he would have had to attract the votes of all new voters, all the votes of his former centrist opponent, and up to 44 percent of those who voted for reformist candidates in 2005,” said Thomas Rintoul, one of the study’s authors.

The leadership of the Islamic republic takes voting very seriously as a symbol of legitimacy and loyalty to the system. Voting always occurs on a day off, to maximize turnout.