Afghan president Hamid Karzai wants a meeting of the nation's elders to decide if US troops staying in the country after 2014 would be immune from prosecution.
Mr Karzai made the proposal after returning from Washington, where he met last President Barack Obama over the future of the alliance between the two countries.
This was also the first time Mr Karzai has floated the idea that Afghans should hold a "loya jirga" - a national assembly of elders - to make the decision on US troop immunity.
The United States has said that it needs to maintain sole legal jurisdiction over its forces in Afghanistan as part of the agreement for forces that will stay after 2014. In Iraq, it was the Iraqi government's refusal to grant such jurisdiction that caused US troops to completely quit.
"We want our national sovereignty and the Americans want the safety of their soldiers," Mr Karzai said. "They don't want their soldiers to be under the laws of another country."
He appeared to be trying to strike a conciliatory note, in sharp contrast to the harsh rhetoric and demands ahead of his US trip. However, he stressed that the issue of US troop immunity was not up to his administration to decide.
"The Afghan government cannot make that decision. It is the decision of the people of Afghanistan. So a loya jirga of the people of Afghanistan should decide," he said.
Loya jirgas have traditionally been used in the country to make major decisions. The last was in November 2011, when Mr Karzai called elders together to discuss whether they should enter into negotiations with the US about a long-term partnership agreement.
Mr Karzai's tone throughout his speech was solicitous of the United States, a departure from the rhetoric in which he regularly demanded new rules for his US allies and accused them of trying to occupy his country.
It may have been a sign that statements from the US administration about the possibility of pulling all troops out of Afghanistan in 2014 had caused him to soften his tone. However, it may also indicate that he came out of the meetings in Washington with a sense that his concerns were finally being addressed.