The issue will be central to talks this week as Afghan president Hamid Karzai meets Barack Obama and Defence Secretary Leon Panetta to discuss ways of framing an enduring partnership beyond December 2014, when combat troops are scheduled to be withdrawn.
"The US does not have an inherent objective of 'X' number of troops in Afghanistan," said a White House spokesman. "We have an objective of making sure there is no safe haven for al Qaeda in Afghanistan and making sure the Afghan government has a security force that is sufficient to ensure the stability of the Afghan government."
The US now has 66,000 troops in Afghanistan, down from a peak of about 100,000 as recently as 2010.
The US and its Nato allies agreed in November 2010 they would withdraw all their combat troops by the end of 2014, but they have yet to decide what future missions might be necessary and how many troops they may require. At stake is the risk of Afghanistan's collapse and a return to the chaos of the 1990s that enabled the Taliban to seize power and provide a haven for Osama bin Laden's al Qaeda network.
Fewer than 100 al Qaeda fighters are believed to remain in Afghanistan, although many more are just across the border in Pakistani sanctuaries.
Mr Panetta has said he foresees a need for a US counter-terrorism force in Afghanistan beyond 2014, plus a contingent to train Afghan forces.
He is believed to favour an option that would keep about 9000 troops in the country.
Administration officials have said they are considering a range of options for a residual US troop presence of as few as 3000 and as many as 15,000.