“We are starting this drawdown from a position of strength,” Mr. Obama said. “Al Qaeda is under more pressure than at any time since 9/11.” He said that an intense campaign of drone strikes and other covert operations in Pakistan had crippled Al Qaeda’s original network in the region, leaving its leaders either dead or pinned down in the rugged border between Pakistan and Afghanistan. Of 30 top Qaeda leaders identified by American intelligence, 20 have been killed in the last year and a half, administration officials said.

But the withdrawal of the entire surge force by the end of next summer will significantly change the way that the United States wages war in Afghanistan, analysts said, suggesting that the administration may have concluded it can no longer achieve its loftiest ambitions there.

Mr. Obama acknowledged as much in his remarks. “We will not try to make Afghanistan a perfect place,” he said. “We will not police its streets or patrol its mountains indefinitely. That is the responsibility of the Afghan government.”

Mr. Obama’s decision is a victory for Vice President Joseph R. Biden Jr., who has long argued for curtailing the military operation in Afghanistan. Mr. Obama indicated a willingness to move toward more focused covert operations of the type that the United States is conducting in Pakistan, Yemen and elsewhere. “When threatened, we must respond with force,” he said. “But when that force can be targeted, we need not deploy large armies overseas.”

The pace of the withdrawal is a setback for the president’s top commander in Afghanistan, Gen. David H. Petraeus, who has been named director of the Central Intelligence Agency. General Petraeus did not endorse the decision, said another official. Defense Secretary Robert M. Gates argued publicly against a too-hasty withdrawal of troops, but he said in a statement on Wednesday that he supported Mr. Obama’s decision.

During the internal debate, Secretary of State Hillary Rodham Clinton also expressed reservations about the scale of the reductions, officials said.

General Petraeus had recommended limiting withdrawals to 5,000 troops this year and another 5,000 over the winter.