Speaking at a briefing by military commanders at Bagram Air Base, Obama said one of the reasons for his visit was to discuss the U.S. footprint for the rest of this year - when the bulk of troops are scheduled to be withdrawn - and afterward.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 Bagram for a brief, surprise visit.
Obama also planned to deliver remarks to troops and to visit wounded soldiers at Bagram, which is the main U.S. base in Afghanistan.
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's Afghan visit is 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 Afghanistan 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.
Obama's deputy national security adviser, Ben Rhodes, said Karzai was to have been informed about the visit shortly before Obama's arrival.
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.
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 when he got off the plane, Obama was also joined by national security adviser Susan Rice and special counselor John Podesta, who has a son stationed in Afghanistan.
Obama inherited two wars from his Republican predecessor, George W. Bush, when he took office for his first term in 2009. He ended U.S. involvement in Iraq, a war he opposed, and his visit to Bagram was seen as a final trip to Afghanistan to salute American forces who are to leave soon.
In recent months he has recognized the valor of troops who faced combat in both Iraq and Afghanistan and earlier this month he was on hand for the formal dedication of the National September 11 Memorial Museum in New York at the site where the World Trade Center towers were brought down by hijacked-plane attackers in 2001.
On June 6, Obama will be in France to mark the 70th anniversary of the D-Day invasion when U.S. and Alllied troops stormed ashore and turned back the Germans. He calls the veterans of the Afghan conflict "the 9/11 generation, that has proven itself to be one of America's greatest."
The controversy involving the Veterans Administration has been particularly biting for Obama because he and his wife, Michelle, have stressed the need to take care of veterans.
"This is more than a government failure. It is a violation of a solemn vow. And the buck stops with the president of the United States," said Vietnam War-veteran and Republican Senator John McCain in an opinion article for the Wall Street Journal.