WASHINGTON — Uneasy allies, President Barack Obama and Afghan President Hamid Karzai demonstrated Friday they could agree on one big idea: After 11 years of war, the time is right for U.S. forces to let Afghans do their own fighting. U.S. and coalition forces will take a battlefield back seat by spring and, by implication, go home in larger numbers soon thereafter.

“It will be a historic moment,” Obama declared.

In a White House meeting billed as a chance to take stock of a war that now ranks as America’s longest, Obama and Karzai agreed to accelerate their timetable for putting the Afghanistan army in the lead combat role nationwide. It will happen this spring instead of summer — a shift that looks small but looms larger in the debate over how quickly to bring U.S. troops home and whether some should stay after combat ends in 2014.

The two leaders also agreed that the Afghan government would be given full control of detention centers and detainees. They did not reach agreement on an equally sticky issue: whether any U.S. troops remaining after 2014 would be granted immunity from prosecution under Afghan law. Immunity is a U.S. demand that the Afghans have resisted, saying they want assurances on other things — like authority over detainees — first.

At a joint news conference with Karzai in the White House East Room, Obama said he was not yet ready to decide the pace of U.S. troop withdrawals between now and December 2014. That is the target date set by NATO and the Afghan government for the international combat mission to end. There are now 66,000 U.S. troops there.

Obama’s message was clear: The Afghans must now show they are capable of standing on their own.

“By the end of next year, 2014, the transition will be complete — Afghans will have full responsibility for their security, and this war will come to a responsible end,” he said, noting that more than 2,000 Americans have died since the war began in October 2001.

The Afghan army and police now have 352,000 in training or on duty, although that number is viewed by many as unsustainable because the government is almost entirely reliant on international aid to pay the bills.

Some private security analysts — and some in the Pentagon — worry that pulling out to quickly will leave Afghanistan vulnerable to collapse. In a worst-case scenario, that could allow the Taliban to regain power and revert to the role they played in the years before the Sept. 11, 2001, attacks as protectors of al-Qaida terrorists bent on striking the U.S.

Many Americans, however, are weary of the war and skeptical of any claim that Afghanistan is worth more U.S. blood.

In a reflection of the diminishing support in Congress for a robust U.S. role in Afghanistan, Sen. Joe Manchin, D-W.Va., a member of the Armed Services Committee, sent a letter to Obama on Friday urging him to significantly reduce the number of American troops in the region and bring American forces home as quickly as possible.

“Our troops have accomplished their mission: Osama bin Laden is dead, extremist networks in Afghanistan have been disrupted so that they are no longer a credible international threat and the Afghan security forces have received training and equipment for nearly a decade,” Manchin wrote. “It is now time to let Afghanistan determine its own future.”

Obama and Karzai also have to decide whether a residual U.S. force will remain after 2014 to prevent al-Qaida from re-establishing a substantial presence in Afghanistan and to continue training and advising Afghan forces. U.S. commanders have recommended that 6,000 to 15,000 U.S. troops remain for those purposes, but the White House seems to believe the true need is closer to 3,000 — or possibly even zero.

Asked at the news conference about a potential post-2104 U.S. military presence, Karzai said, “Numbers are not going to make a difference to the situation in Afghanistan. It’s the broader relationship that will make a difference.”

Although it’s not widely recognized in the U.S., American forces have greatly scaled back their combat role already. In a joint statement, Obama and Karzai said Afghan forces now lead more than 80 percent of combat operations, and by next month they will be in the lead in security for nearly 90 percent of the Afghan population.

Once the Afghans take the lead across the country this spring, “most unilateral U.S. combat operations should end, with U.S. forces pulling back their patrols from Afghan villages,” the leaders said in a joint statement. They added that this puts greater importance on providing the Afghans “appropriate equipment and enablers,” although they made no mention of specific new agreements to equip the Afghan army or police.

“Starting this spring our troops will have a different mission: training, advising and assisting Afghan forces,” Obama said.

He added later that even in a backup role he could not rule out that U.S. troops could be drawn into combat.

“The environment is going to still be very dangerous,” Obama said. But he emphasized that the main role of U.S. forces starting this spring will be support, such as training and advising.

Karzai said he was pleased by the agreement, in part because it means that by spring there will be no foreign troops in Afghan villages. That implies an end to a U.S.-led program in which U.S. special operations forces have moved into rural villages in small numbers to quietly build the beginnings of local resistance to the Taliban.

In their statement the leaders said they discussed the possibility of a continued U.S. troop presence beyond December 2014, when the U.S. and allied combat mission is to end. But they did not settle on any specifics.

Friday’s meeting was the first between Obama and Karzai since November’s U.S. presidential election.