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* Obama yet to decide on post-2014 troop presence
* Says future U.S. mission will be limited, eyes on al Qaeda
* NATO to formally conclude combat mission at end of 2014 (Rewrites with Obama's address)
By Phil Stewart and Tabassum Zakaria
WASHINGTON, Feb 12 (Reuters) - President Barack Obama announced on Tuesday that 34,000 troops - about half the U.S. force in Afghanistan - will withdraw by early 2014, bringing the United States one step closer to wrapping up the costly, unpopular war.
Obama announced the withdrawal in his annual State of the Union address, as he renewed his pledge to a war-weary American public that the 66,000 remaining U.S. troops in Afghanistan would move into a support role this spring.
"This drawdown will continue. And by the end of next year, our war in Afghanistan will be over," Obama said to applause.
The announcement was limited in detail and appeared to give the White House time and flexibility before it answers bigger questions about its exit strategy from America's longest war.
This includes the size of the U.S. force that Obama will keep in Afghanistan once the NATO mission is completed and the war is declared formally over at the end of 2014.
Obama also must decide how large an Afghan force to finance, and for how long, as his allies in Congress press to keep them at their maximum strength.
No decisions on broader issues have been made, a senior administration official said, and Obama said only that the future U.S. mission would be focused on training and equipping Afghan forces and combating al Qaeda.
"Beyond 2014, America's commitment to a unified and sovereign Afghanistan will endure, but the nature of our commitment will change," Obama said.
The announcement came a month after Obama and Afghan President Hamid Karzai agreed in Washington on a plan to slightly speed up the handover of combat operations in Afghanistan, with Afghan forces taking the lead role throughout the country this spring.
How the Afghan forces fare in this leading role has yet to be seen. Although U.S. military officials express confidence in growing Afghan capabilities, Afghan forces remain highly dependent on U.S. support.
Outgoing Defense Secretary Leon Panetta welcomed the decision and said the plan to continue drawing down American forces in a phased approach over the coming year was recommended by the former commander in Afghanistan, General John Allen.
Allen's successor, General Joseph Dunford, "will have the combat power he needs," Panetta assured in a statement.
Another U.S. official, speaking on condition of anonymity, said U.S. commanders would have the flexibility to decide when to withdraw the 34,000 troops, as long as they were out by early next year, meaning the bulk of them could stay through this year's peak fighting months.
Jeffrey Dressler of the Institute for the Study of War, a Washington think-tank, said such flexibility would allow the military to "focus on the fight at hand" during the summer and early fall.
Still, he described the removal 34,000 troops as a "tall task" that comes at a challenging time for Afghan forces.
"The real question now is what the post-2014 presence will be, which in my mind, is a far more important question," Dressler said.
Previous discussions at the White House focused on a range of options of between 3,000 and 9,000 troops, with military commanders most comfortable with the higher-end figures.
It was unclear when Obama might make a decision.
Bruce Riedel, who chaired Obama's 2009 review of Afghan policy and is now at the Brookings Institution think-tank in Washington, said a crucial factor will be the extent to which al Qaeda's core leadership in Pakistan continues to degrade.
A stronger al Qaeda in neighboring Pakistan means the United States would need a more robust counter-terrorism presence, for example, he said.
"The president is rightly not making that decision now when he doesn't have to," said Riedel, who heads the Intelligence Project at Brookings.
"He should wait and see how much success we have against (al Qaeda core)." (Editing by Jackie Frank, Bill Trott, Cynthia Osterman and Lisa Shumaker)