The United States is considering pulling out all its troops from Afghanistan next year, amid tension between the Obama administration and President Hamid Karzai's government.
President Barack Obama is committed to wrapping up US military involvement in Afghanistan by the end of 2014.
But the United States has been talking with officials in Afghanistan about keeping a small residual force there of perhaps 8000 troops.
US officials are not denying a report that Mr Obama has become increasingly frustrated by his dealings with Mr Karzai, Reuters reports.
Their relationship fell to new depths after a US move in June this year to open peace talks with the Taliban, leading Mr Karzai to suspend talks on a security pact between the allies.
A video conference on 27 June between Mr Obama and Mr Karzai aimed at lowering tensions ended poorly, the New York Times reported, citing US and Afghan officials with knowledge of the conversation.
However, senior Afghan figures close to Mr Karzai were sceptical that Washington would consider a complete withdrawal.
More than a dozen American troops were killed in Afghanistan in June. The number of troops, now about 63,000, already is set to decline to 34,000 by February 2014. The White House has said the great majority of American forces would be out by the end of next year.
US troops have been in Afghanistan since 2001. The US invaded Afghanistan to topple the Taliban who had harboured the al Qaeda network responsible for the September 11 attacks on New York and Washington weeks earlier.