BAGRAM AIR FIELD, Afghanistan (AP) — President Barack Obama, on a surprise holiday visit to this sprawling military base, said Sunday he was close to a decision about the number of U.S. troops who will remain after year's end in America's longest war.

"We are aware of the sacrifices so many have made," Obama said after a briefing by Marine Gen. Joseph F. Dunford, the top American commander in Afghanistan. "We'll probably be announcing some decisions fairly shortly."

The decision may come Wednesday when Obama delivers the commencement address at the U.S. Military Academy in West Point, New York.

Air Force One landed at Bagram Air Field, the main U.S. base in Afghanistan, after an overnight flight from Washington. Obama was scheduled to spend just a few hours on the base and had no plans to travel to Kabul, the capital, to meet with Hamid Karzai, the mercurial president who has had a tumultuous relationship with the White House.

Obama's surprise trip came as the U.S. and NATO withdraw most of their forces ahead of a year-end deadline.

Obama is seeking to keep a small number of U.S. troops in Afghanistan beyond 2014 to train Afghan security forces and conduct counterterrorism missions. But that plan is contingent on Karzai's successor signing a bilateral security agreement that Karzai has refused to authorize.

Ben Rhodes, Obama's deputy national security adviser, said Obama had not finalized the troop decision and no announcement was expected during the Afghanistan visit.

At least 2,181 members of the U.S. military have died during the nearly 13-year Afghan war and thousands more have been wounded. There are still about 32,800 U.S. troops in Afghanistan, down from a high of 100,000 in mid-2010, when as Obama sent in additional soldiers to quell escalating violence.

Obama said he saw a poster of the Twin Towers, downed in the 2001 terrorist attacks, when he arrived at the briefing building. "It's a reminder of why we're here," he said.

This was Obama's fourth visit to Afghanistan as president, but his first since winning re-election in 2012.

Rhodes said Obama was passing on a meeting with Karzai in order to avoid injecting himself into Afghanistan's presidential elections. Karzai was given advance notice of Obama's trip, Rhodes said, though it was unclear how far ahead of time.

In addition to the briefing by U.S. commanders in Afghanistan, Obama planned to speak to troops at Bagram and visit the injured being treated at a base hospital.

Obama was accompanied by a few advisers, including senior counselor John Podesta, whose son is serving in Afghanistan. Also along was country singer Brad Paisley, who was to perform for U.S. troops.

As is typical of recent presidential trips to war zones, the White House did not announce Obama's visit in advance. Media traveling with Obama for the 13-hour flight had to agree to keep the trip secret until the president arrived at the air base.

Obama's visit was taking place against the backdrop of growing outrage in the United States over the treatment of America's war veterans. More than two dozen veterans' hospitals across America are under investigation over allegations of treatment delays and deaths, putting greater scrutiny on the Department of Veterans Affairs. The agency already was struggling to keep up with the influx of forces returning home from Afghanistan and Iraq.

Obama has staked much of his foreign policy philosophy on ending the two wars he inherited from his predecessor, George W. Bush.

The final American troops withdrew from Iraq in the closing days of 2011 after the U.S. and Iraq failed to reach a security agreement to keep a small American residual force in the country. In the years that have followed the American withdrawal, Iraq has been battered by resurgent waves of violence.

U.S. officials say they're trying to avoid a similar scenario in Afghanistan. While combat forces are due to depart at the end of this year, Obama administration officials have pressed to keep some troops in Afghanistan after 2014 to continue training the Afghan security forces and undertake counterterrorism missions.

Pentagon officials have pushed for as many as 10,000 troops; others in the administration favor as few as 5,000 troops. Obama has insisted he will not keep any Americans in Afghanistan without a signed security agreement that would grant those forces immunity from Afghan law.

U.S. officials had hoped plans a post-2014 force would be well underway by this point. But Karzai stunned U.S. officials this year by saying he would not sign the security agreement even though he helped negotiate the terms. The move signaled that Karzai does not want his legacy to include a commitment to allow the deployment of international troops in his country any longer.

Karzai's decision compounded his already tense relationship with officials in Washington who have grown increasingly frustrated by his anti-American rhetoric and decision to release prisoners over the objections of U.S. officials. Obama and Karzai have spoken just once in the past year.

Karzai, the only president Afghans have known since the 2001 U.S.-led invasion to topple the Taliban's Islamic rule, was constitutionally barred from running for a third term this year. An election to choose his successor was held this month, with the top two candidates advancing to a June runoff.

Both of those candidates, former Foreign Minister Abdullah Abdullah and ex-Finance Minister Ashraf Ghani Ahmadzai, have promised a fresh start with the West and pledged to move ahead with the security pact with the U.S.