The talks between Burns and Afghanistan's Foreign Minister Zalmai Rasoul are the second round of negotiations over the provisions of the Strategic Partnership Agreement, a set of principles and general commitments signed in May 2012 by President Barak Obama and Afghan President Hamid Karzai. Delegates first met in Washington in October.
Sticking points may include the amount of funds the US provides to Afghan security forces. The two countries are also still squabbling over a separate agreement that would protect from prosecution a residual force of as many as 10,000 US troops who would stay behind after the final withdrawal.
In remarks before the meeting at the foreign ministry, Burns promised that Washington would stick by Afghanistan and its nascent national security forces after 2014 and the end to the international combat mission.
More From This Section
Karzai's election in 2009 was marred by widespread allegations of corruption, vote tampering and election fraud.
He denied the charges but the acrimonious aftermath tainted his relationship with the West, which was the most vocal of his critics.
The pact emphasizes a free, fair and transparent election in 2014. Karzai however has been relentless in his criticism of US involvement in Afghanistan's political process, alleging Washington was maneuvering secretly to strengthen his political opposition even though he cannot run for a third term.
Burns also repeated Washington's support for the opening of an office for the Taliban in the Middle Eastern State of Qatar to provide a venue where Karzai's High Peace Council could meet Taliban representatives to try to find a peaceful end to the 12-year war.
Yet the Taliban have met representatives of about 30 countries, participated in international forums in Tokyo and France, and held backdoor talks with Afghanistan's opposition politicians.