The White House has said for the first time it is possible that no US troops will remain in Afghanistan past 2014, as President Hamid Karzai arrived in Washington for talks with Barack Obama.
Ben Rhodes, a top US security official, told reporters the administration was still considering a range of options.
Mr Karzai's three-day trip will include crucial talks with Mr Obama and other officials, but no final decision.
The Afghan president wants US troops out of Afghan towns and villages.
Correspondents say the meeting comes as relations between the two countries have been more fractious than usual.
The BBC reports important issues are on the agenda during this visit. The number and scope of US soldiers in post-2014 Afghanistan is one. Mr Karzai will also demand that his country's sovereignty be respected.
He wants the US to rescind control of Afghan airspace, stop raids on villages, and hand over prisoners and detention centres it still controls. The future size and focus of the Afghan military is also on the agenda.
The two leaders will also discuss talks with the Taliban and the opening of a formal Taliban political office, most probably in Qatar. President Karzai will insist on a peace process which is truly Afghan-led.
President Karzai will not stand in next year's presidential elections. Both sides will be keen to ensure this political transition - widely seen as no less important than the security handover - goes smoothly.
As of December, NATO forces in Afghanistan numbered 102,000, including 68,000 US troops.