WASHINGTON — The Obama administration is discussing whether to reduce U.S. forces in Afghanistan by at least an additional 20,000 troops, possibly even more, by 2013, reflecting a growing belief within the White House that the mission has reached the point of diminishing returns.

Accelerating the withdrawal of U.S. forces has been under consideration for weeks by senior White House officials, but those discussions are now taking place in the context of two significant setbacks to U.S. efforts in Afghanistan — the killings Sunday of Afghan civilians by an Army staff sergeant and the violence touched off by last month's burning of Qurans by U.S. troops.

Administration officials cautioned Monday that no decisions on additional troop cuts have been made, and President Obama reaffirmed his commitment to the Afghan mission despite the recent setbacks, warning against "a rush for the exits" amid questions about the U.S. war strategy.

"It's important for us to make sure that we get out in a responsible way, so that we don't end up having to go back in," Obama said in an interview with KDKA in Pittsburgh.

Any accelerated withdrawal would face stiff opposition from military commanders who want to keep the bulk of the remaining U.S. troops in Afghanistan until the end of 2014, when the NATO mission there is supposed to end.

The United States has nearly 90,000 troops in Afghanistan, with 22,000 due home by September.

There has been no schedule set for the withdrawal of the remaining 68,000 U.S. troops, although Obama said last year the drawdown would continue "at a steady pace" until the United States handed over security to the Afghan forces in 2014.

At least three options are under consideration, according to officials at the White House, the Pentagon and the State Department.

One plan, backed by Thomas Donilon, the national-security adviser, would be to announce that at least 10,000 more troops would come home by the end of December, then 10,000 to 20,000 more by June 2013.

Vice President Joseph Biden has been pushing for a bigger withdrawal that would reduce the bulk of the troops around the same time the mission shifts to a support role, leaving behind Special Operations teams to conduct targeted raids.

Obama's military commanders, meanwhile, want to maintain troops in Afghanistan as long as possible.

If cuts have to be made, the commanders favor making them at the end of 2013, after the fighting season largely is finished.

Any troop cuts made midyear would mean those forces would not be available during the main fighting season, which runs from spring to early fall.

"We've come up with several options, but they're back-of-the-envelope options," said a senior U.S. military official who said the internal discussions were beginning to focus on the costs, logistics and security risks of each plan.

Obama will discuss the NATO mission in Afghanistan when he meets with British Prime Minister David Cameron on Tuesday and Wednesday in Washington.

A European official said Monday it was imperative that the United States and its NATO partners project a public face to the Afghans that, while NATO troops will be leaving Afghanistan, the West will not abandon the country.

"The most important thing now is the messaging," the official said.