But since his re-election, Mr. Obama has confronted the question of how to stay true to his pledge to wind down the war without undermining the still-fragile military gains. Presidents in their second terms often tend to think about their foreign policy legacy, and the conflict in Afghanistan, unlike in Iraq, has come to be known as Mr. Obama’s war.

The troop withdrawal question came to the fore last month after Mr. Obama met with President Hamid Karzai of Afghanistan in Washington, where Mr. Obama said he would accelerate the transfer of responsibility for security to the Afghans this year.

As he had done before, Mr. Obama set the parameters of the deliberations over the troop level by issuing planning guidance to the Pentagon. Operating on the basis of those presidential instructions, which the White House has not made public, General Allen prepared three options. Administration officials said that the White House had essentially endorsed the general’s preferred option — what Defense Secretary Leon E. Panetta said in a statement was General Allen’s “phased approach.”

According to the new withdrawal schedule, the number of troops is to go down to 60,500 by the end of May. By the end of November, the number will be down to 52,000. By the end of February 2014, the troop level is to be around 32,000.

The February 2014 number is less than some military officers had hoped would be on hand when the Afghan presidential election is held that April. But that seems to be more than offset by the decision to allow the military to keep the bulk of its force through the 2013 fighting season.

“The intensity of combat in the warmer months is twice what it is in colder months,” said Michael E. O’Hanlon, a military expert at the Brookings Institution. “For the next eight months, it is as good an outcome as proponents of the current strategy could have had.”