* Obama mindful of war-weary public as he winds down in Afghanistan
* White House not ruling out removing all troops after 2014
* Progress expected with Karzai but no firm decisions - Obama aides
By Matt Spetalnick
WASHINGTON, Jan 11 (Reuters) - President Barack Obama and Afghan President Hamid Karzai will hold a critical round of talks on Friday that could help determine how fast the United States withdraws troops from Afghanistan and whether it leaves a residual force after 2014.
Hosting Karzai at the White House, Obama faces the challenge of pressing ahead with his re-election pledge to continue winding down the long war in Afghanistan while preparing the Afghan government to prevent a slide back into chaos and a Taliban resurgence once most NATO forces are gone.
Karzai's visit, which follows a year of growing strains in U.S.-Afghan ties, comes amid stepped-up deliberations in Washington over the size and scope of the U.S. military role in Afghanistan once the NATO-led combat mission concludes at the end of next year.
White House officials have left open the possibility of a complete U.S. withdrawal after 2014 - as happened in Iraq in 2011 - an option that conflicts with the Pentagon's view that thousands of troops will be needed to bolster and train still-fragile Afghan security forces.
But talk of this "zero option" may actually be a gambit to squeeze concessions from Karzai, who has yet to agree on immunity from prosecution for any U.S. forces that stay behind under a bilateral security pact being negotiated. It could also send a message to the Pentagon to scale back expectations of future troop levels.
The White House believes Obama and Karzai, despite a history of sometimes tense relations, can narrow their differences. But Obama aides expect no breakthroughs or concrete agreements and say it will be months before Obama decides how many troops - if any - he wants to keep in Afghanistan.
U.S. officials have said privately that the White House is asking for options to be developed for keeping between 3,000 and 9,000 troops in the country. General John Allen, the top U.S. and NATO commander in Afghanistan, had initially suggested that as many as 15,000 troops should remain.
With some 66,000 U.S. troops currently in Afghanistan, Obama is also deciding on the pace of this year's troop reductions. Afghan forces are due to take the lead role in security across the country in 2013.
"WAR OF NECESSITY"
Obama once called Afghanistan a "war of necessity" but is heading into a second term looking for an orderly way out of the conflict, which was sparked by the Sept. 11, 2001, attacks by al Qaeda on the United States.
Former Senator Chuck Hagel, Obama's nominee to become defense secretary, is likely to favor a sizable troop reduction.
Deliberations between Obama and his aides on winding down the unpopular war will have to compete with other priorities dominating his agenda, including the next round of U.S. fiscal showdowns and an intensifying push for gun-control measures.
Many of Obama's Republican opponents have criticized him for setting a timetable for withdrawal from Afghanistan and accuse him of undercutting the U.S. mission by reducing the size of the U.S. force there too quickly.
Karzai's talks with Obama - together with a working lunch and joint news conference - will cap a series of meetings this week with Defense Secretary Leon Panetta, Secretary of State Hillary Clinton and top lawmakers.
"After a long and difficult past, we finally are, I believe, at the last chapter of establishing ... a sovereign Afghanistan that can govern and secure itself for the future," Panetta told Karzai at the start of talks at the Pentagon on Thursday.
Clinton and Karzai met at the State Department on Thursday evening and were to have a working dinner.
Also on the agenda for the Obama-Karzai talks are tentative reconciliation efforts involving Taliban insurgents. Those efforts have shown flickers of life after nearly 10 months of limbo.
Karzai and his U.S. partners have not always seen eye to eye, even though the American military has been seen as crucial to securing his tenure from insurgents' attempts to oust him.
In October, Karzai accused the United States of playing a double game by fighting the war in Afghan villages instead of going after those in Pakistan who support insurgents.