"Over the last three years, the tide has turned," Obama said at Bagram Air Base after slipping into the country under the cover of darkness to ink the agreement with Afghan President Hamid Karzai.
"We broke the Taliban's momentum. We've built strong Afghan security forces. We devastated al Qaeda's leadership, taking out over 20 of their top 30 leaders. And one year ago, from a base here in Afghanistan, our troops launched the operation that killed Osama bin Laden."
He added: "The goal that I set — to defeat al Qaeda, and deny it a chance to rebuild — is within reach."
Obama paid the surprise visit to Afghanistan as his friends and foes back home duked it out over whether he was taking too much credit for the Pakistani raid by navy SEALs a year ago that finally took out bin Laden, the mastermind of the Sept. 11, 2001 terrorist attacks.
Obama's re-election campaign has been criticized in recent days, even from usually friendly quarters, for a new ad that essentially questions whether Republican presidential front-runner Mitt Romney would have had the cajones to OK the raid if he'd been in the Oval Office at the time.
A day after saying "even Jimmy Carter" would have authorized such a raid, Romney called the video "silly" on Tuesday.
"Any thinking American would have ordered the exact same thing," Romney said on CBS's "This Morning." "Let's not make the capture and killing of Osama bin Laden a politically divisive event."
Romney issued a statement on Tuesday congratulating Obama on the bin Laden anniversary while adding that the raid "was the culmination of nearly a decade of hard work and sacrifice by our men and women in the military and intelligence communities."
The former Massachusetts governor spent the day in New York, ostensibly "not politicizing" the event by handing out pizzas for firefighters alongside Rudy Giuliani, a one-time Republican nominee himself who was the city's mayor during the 9-11 attacks.
Despite that messaging inconsistency, others have joined Romney in warning against making political hay out of bin Laden's death, an event that prompted thousands of Americans to take to the streets to celebrate a year ago.
"I do worry a great deal ... that somehow this gets spun into election politics," Mike Mullen, chairman of the Joint Chiefs of Staff, told NBC in an interview scheduled to air on Wednesday night.
"I can assure you that those individuals who risk their lives — the last thing in the world that they want is to be spun into that. So I'm hoping that that doesn't happen."
Defense Secretary Robert Gates, meantime, has called the raid "one of the most gutsy decisions made by a U.S. president." Gates also served under George W. Bush.
Obama has defended the bin Laden ad. In remarks at the White House on Monday, he pointed to previous Romney statements that suggested the U.S. should stop focusing on snagging bin Laden.
"It's not worth moving heaven and Earth spending billions of dollars just trying to catch one person," Romney said in 2007 during his first run for president.
Romney should now explain himself, Obama suggested.
"I'd just recommend that everybody take a look at people's previous statements," Obama said.
"I assume that people meant what they said when they said it. I said that I'd go after bin Laden if we had a clear shot at him, and I did. ... If there are others who have said one thing, and now suggest they'd do something else, then I'd go ahead and let them explain it."
Britain's Daily Mail, however, is reporting that the Navy SEALs themselves are resentful that Obama is using the raid for political purposes.
"The operation itself was great and the nation felt immense pride. It was great that we did it," Chris Kyle, a former SEAL sniper, told the newspaper.
"But bin Laden was just a figurehead. The war on terror continues. Taking him out didn't really change anything as far as the war on terror is concerned and using it as a political attack is a cheap shot."
Others have expressed dismay that Republicans, of all people, are taking issue with Obama given they've been accused for years of using 9-11 and its aftermath for political purposes.
After U.S. forces toppled Iraqi dictator Saddam Hussein in 2003, Bush gave a speech aboard a U.S. aircraft carrier in front of a banner emblazoned with the words: Mission Accomplished.
A year later, he often pointed to his success in ridding the world of Saddam as he ran for re-election, while Dick Cheney, his vice-president, warned Americans that if they elected Democratic presidential nominee John Kerry, another terrorist attack was likely.
With the 2012 presidential election just seven months away, Obama can now argue he's brought two monstrously expensive and unpopular wars to an end in addition to nabbing the notorious terrorist whose attacks on the United States 11 years ago spurred those conflicts.
"I recognize that many Americans are tired of war," he said.
"As president, nothing is more wrenching than signing a letter to a family of the fallen, or looking in the eyes of a child who will grow up without a mother or father. I will not keep Americans in harm's way a single day longer than is absolutely required for our national security."Suggest a correction