BAGRAM AIRBASE - 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for his trip was to discuss the US footprint for the rest of this year - when the bulk of troops are scheduled to be withdrawn - and afterward."We'll probably be announcing some decisions fairly shortly," said Obama, who flew into the main US base in Afghanistan for a brief, surprise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 US 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.In an indication of the frayed relations between the Obama administration and the Karzai government, the Afghan president rejected an invitation extended through the USembassy 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 to 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 US troops behind in Afghanistan for training Afghan forces and counter-terrorism operations, after the formal US 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 US phone surveillance programme, saying it violates his country's sovereignty.In his remarks to troops at Bagram, Obama said he was hopeful that the US-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 US military to train Afghan forces, Obama administration officials briefed on the matter say.There are now about 33,000 US 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.Obama told the top US General in Afghanistan Joseph Dunford and the US ambassador to Kabul James Cunningham that he was facing tough decisions on the US posture after the end of the year when all combat troops pull out.US officials said as Obama flew into Afghanistan aboard Air Force One that they believed that both candidates in Afghanistan's run-off election, Ashraf Ghani and Abdullah Abdullah, would sign a bilateral security agreement that would allow US troops to stay.This news was published in The Nation newspaper. Read complete newspaper of 26-May-2014 here.