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

Accelerating the withdrawal of United States forces has been under consideration for weeks by senior White House officials, but those discussions are now taking place in the context of two major setbacks to American efforts in Afghanistan — the killings on Sunday of Afghan civilians attributed to a United States Army staff sergeant and the violence touched off by burning of Korans last month by American troops.

Administration officials cautioned on Monday that no decisions on additional troop cuts have been made, and in a radio interview President Obama reaffirmed his commitment to the Afghan mission in spite of the recent setbacks, warning against “a rush for the exits” amid questions about the American 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,” Mr. 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 American troops in Afghanistan until the end of 2014, when the NATO mission in Afghanistan is supposed to end. Their resistance puts Mr. Obama in a quandary, as he balances how to hasten what is increasingly becoming a messy withdrawal while still painting a portrait of success for NATO allies and the American people.