The Northern Alliance says it is ready to transfer power to a UN-backed transitional council.
The Alliance also says leader Burhanuddin Rabbani will not be the head of that new body.
The Alliance's foreign minister, Dr Abdullah, also says his group is prepared to "be flexible" on the issue of international peacekeepers in Afghanistan.
They will require a UN mandate that their stay in the country should be limited, he added.
"We are ready to transfer power to a transitional authority and the head of the transitional authority will not be the head of the Islamic State of Afghanistan," Abdullah said, referring to Rabbani.
The Alliance is facing strong international pressure to break a deadlock in talks underway near Bonn on Afghanistan's political future.
Alliance delegates in Germany had been stalling on providing names of people it wants to serve in an interim administration.
During his press conference, Abdullah did not state unequivocally that the names would be provided. Instead, he said "there will be discussion on names" as well as other details "in the coming days."
"We think the results are promising," he said of the Germany talks. "All those issues will be worked out in coming days."