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Afghan officials on Monday canceled Saturday’s run-off presidential vote after the withdrawal from the race of the last challenger, Abdullah Abdullah, and declared President Hamid Karzai to be the winner of the country’s fraught elections.

Azizullah Ludin, the chairman of Afghanistan’s election commission, said the Constitution did not require a run-off and the vote had been canceled, contrary to the publicly expressed wishes of Mr. Karzai. Mr. Ludin cited security and financial concerns about the cost of the vote.

Mr. Karzai and Afghanistan’s Independent Election Commission had been under intense pressure from Afghanistan’s international backers, including the United States, to cancel the second round of voting because of fears relating to security and a...