US Secretary of State John Kerry and Afghan President Hamid Karzai extended talks on Saturday as part of a last-ditch effort to negotiate a security pact that would determine, among other things, how many US troops stay after 2014.
Talks had hit a wall over two sticking points that the United States hopes will be ironed out by the end of the month, a deadline previously set for signing the deal.
"We will try to see if we can make a little more progress, which we have been doing," Kerry told reporters and US embassy staff.
Karzai's spokesman, Aimal Faizi, told reporters: "There are still issues we are finalising, therefore there is a need for a third round of talks this evening."
While the United States is keen to conclude the negotiations quickly, the Afghan president has said the pact can wait until after Afghan elections, due in April.
Progress towards an agreement was made on the first day of talks, on Friday, according to both Afghan and US officials.
An agreement appeared to have been reached on the first of the two sticking points - a US request to run independent counter-terrorism missions on Afghan territory.
The focus of the talks had turned to the second contentious point, a US refusal to guarantee protection from foreign forces, which it wants to avoid as it could require taking offensive action against its ally Pakistan, an Afghan official said.
Most foreign combat troops are due to leave Afghanistan by the end of 2014 and without a deal, the United States could pull out all of its forces in an outcome known as the "zero option", which was unthinkable until a few months ago.
The collapse of similar talks between the United States and Iraq in 2011 - triggered partly by Baghdad's refusal to provide immunity to US soldiers serving there - led to the United States pulling its troops out of the country.
Afghan security has been deteriorating, increasing worry about the country's prospects after Western forces leave. On Saturday, a car bomb killed four people in the eastern city of Jalalabad.
Efforts to draw the Taliban into negotiations have come to nothing. The militants say they will fight on until all foreign forces leave and they dismiss Karzai as a US "puppet."