(Adds Obama to troops in paragraph 5,15 and Karzai aide in paragraphs 9-10)
By Steve Holland
BAGRAM AIR BASE, Afghanistan, May 25 (Reuters) - President Barack Obama, on a visit to Afghanistan, said on Sunday his administration would likely announce soon how many troops the United States will keep in the country, as it winds down its presence after nearly 13 years of war.
Speaking at a briefing by military commanders at Bagram Air Base, Obama said one reason for his trip was to discuss the U.S. footprint for the rest of this year - when the bulk of troops are scheduled to be withdrawn - and afterward.
"We'll probably be announcing some decisions fairly shortly," said Obama, who flew into the main U.S. base in Afghanistan for a brief, surprise visit.
The trip on Memorial Day weekend, his fourth visit to Afghanistan, comes as Obama is buffeted by criticism at home that his handling of foreign policy has been too passive in dealing with crises from Syria to Ukraine and Russia. He is to respond to the criticism in a speech on Wednesday at the U.S. Military Academy at West Point.
Obama also delivered remarks to troops at Bagram, getting hollers from the crowd as he told them, "I'm here on a single mission and that is to thank you for your extraordinary service." He was also set to visit wounded soldiers.
His trip was bound to be seen by some critics as an attempt to redeem himself in the eyes of military veterans who are alarmed at allegations that government-run medical facilities in the United States have not provided timely care for veterans.
At Bagram, Obama was briefed by Army General Joseph Dunford, who heads U.S. and NATO forces in Afghanistan, and U.S. Ambassador to Afghanistan James Cunningham.
NO PLANS TO VISIT KARZAI
Obama had no plans to visit the Afghan capital Kabul or meet President Hamid Karzai and other government officials during a trip expected to last only a few hours. This allows him to avoid getting immersed in the country's presidential election campaign to choose a successor to Karzai, who has long been out of favor in Washington.
In an indication of the frayed relations between the Obama administration and the Karzai government, the Afghan president rejected an invitation extended through the U.S embassy to meet Obama at Bagram, Abdul Karim Khurram, Karzai's chief of staff, told Reuters.
"President Karzai said he would warmly welcome him if he comes to the palace but in no way he would go Bagram to meet him," Khurram said.
Karzai has irked Obama by refusing to sign a bilateral security agreement that Washington wants before it will agree to leave a contingent of U.S. troops behind in Afghanistan for training Afghan forces and counter-terrorism operations, after the formal U.S. troop drawdown.
In turn, Karzai has long expressed anger at civilian deaths in Afghanistan. He told the Washington Post in an interview in March that the war in Afghanistan was not fought with his country's interests in mind.
In a statement issued before Obama's arrival in Afghanistan, Karzai criticized the U.S. phone surveillance program, saying it violates his country's sovereignty.
In his remarks to troops at Bagram, Obama said he was hopeful that the U.S.-Afghan bilateral security agreement would be signed once a new Afghan president was sworn in.
The number of U.S. troops in Afghanistan may drop well below 10,000 - the minimum demanded by the U.S. military to train Afghan forces, Obama administration officials briefed on the matter say.
There are now about 33,000 U.S. troops in Afghanistan, down from 100,000 in 2011, when troop numbers peaked a decade into a conflict in which more than 2,100 Americans have been killed.
Obama left Washington under cover of darkness on Saturday night and flew for more than 13 hours to arrive at Bagram on Sunday night local time. He brought with him country music star Brad Paisley to provide entertainment for the troops.
Wearing an Air Force One bomber jacket, Obama was also joined by national security adviser Susan Rice and special counselor John Podesta, who has a son stationed in Afghanistan.
(Additional reporting by Jeff Mason in Washington and Jessica Donati and Hamid Shalizi in Kabul; Editing by Caren Bohan and Frances Kerry)