Looking to deliver on his 2008 campaign promise to extricate the U.S. from two wars, President Obama on Tuesday night mapped out an agreement for an American withdrawal from Afghanistan.

In a prime-time address from Bagram Air Base in Afghanistan, Mr. Obama called for an end to an era of war.

“My fellow Americans, we have traveled through more than a decade under the dark cloud of war,” the president said. “Yet here, in the pre-dawn darkness of Afghanistan, we can see the light of a new day on the horizon. The Iraq War is over. The number of our troops in harm’s way has been cut in half, and more will be coming home soon. We have a clear path to fulfill our mission in Afghanistan, while delivering justice to al Qaeda.

“This time of war began in Afghanistan, and this is where it will end,” Mr. Obama said.

The president thanked the troops for their service, sacrifice and resilience and said an American renewal is within reach because of them.

“Time and again, they have answered the call to serve in distant and dangerous places,” he said. “In an age when so many institutions have come up short, these Americans stood tall. They met their responsibilities to one another and the flag they serve under. I just met with some of them and told them that, as commander in chief, I could not be prouder. In their faces, we see what is best in ourselves and our country.”

Mr. Obama also had strong words for the Taliban, which in recent weeks dropped out of negotiations with the U.S. for a transition agreement.

“Many members of the Taliban — from foot soldiers to leaders — have indicated an interest in reconciliation,” he said. “A path to peace is now set before them. Those who refuse to walk it will face strong Afghan security forces, backed by the United States and our allies.”

Mr. Obama arrived in Afghanistan under cover of darkness Tuesday on the anniversary of the death of Osama bin Laden, part of a surprise, around-the-globe trip that added drama to what was already a politicized mission.

After midnight in Kabul, Mr. Obama and Afghan President Hamid Karzai signed a 10-page strategic partnership agreement cementing a U.S. support role in Afghanistan for a decade after 2014, when NATO forces are planning to end their combat mission and seriously curtail their presence in the country.

Immediately after signing the agreement, the president took time to meet with the troops and deliver a nine-minute, off-the-cuff speech to an audience of 3,200 service members who were waiting in a hangar for several hours late in the evening before being told Mr. Obama was on his way.

It was the first time Mr. Obama publicly invoked bin Laden’s death since arriving in Afghanistan.

“We did not choose this war. This war came to us on 9/11,” he said. “Because of the sacrifices now of a decade — a new greatest generation — not only were we able to blunt the Taliban’s momentum, not only were we able to drive al Qaeda out of Afghanistan, but slowly and systematically we have been able to decimate the ranks of al Qaeda. And a year ago, we were finally able to bring Osama bin Laden to justice.”

At the mention of bin Laden, the crowd responded with a rousing “hoo-ah.”

The president also acknowledged the difficult struggle troops and their families still face on a daily basis.

“I know it’s still tough. I know the battle’s not yet over. Some of your buddies are going to get injured, and some of your buddies may get killed, and there’s going to be heartbreak and pain and difficulty ahead. But there’s a light on the horizon because of the sacrifices you’ve made.”

The timing of the trip, on the anniversary of bin Laden’s slaying a year ago in Pakistan by a Navy SEAL team, only amplified complaints that Mr. Obama is using the raid for political gain. His campaign last week released an ad questioning whether likely Republican nominee Mitt Romney would have approved the bin Laden mission, prompting harsh criticism from the right and the left that Mr. Obama was playing politics with an event that should bring Americans together.

On Monday, Mr. Obama dismissed criticism that he or his campaign is exploiting the anniversary.

“I hardly think you’ve seen any excessive celebration taking place here,” Mr. Obama said.

Senior administration officials brushed aside those questions during a conference call with reporters Tuesday afternoon before the president’s televised remarks to the nation, arguing that the timing of the trip was driven by the negotiations over the Strategic Partnership Agreement and by the desire of both presidents to sign the agreement in Afghanistan before the NATO summit in Chicago this month.

The president also wanted to spend time with the troops on the anniversary of bin Laden’s death, the officials said.

“It was always the president’s intention to spend the anniversary with the troops,” one official said.

At least 33 U.S. service members were killed in Afghanistan in April, making it the deadliest month this year. U.S. officials insist security has improved in Afghanistan since the troop buildup Mr. Obama ordered at the end of 2009, but there have been a series of deadly incidents in recent months, including riots following the burning of Korans at Bagram, an American base, and a protracted gun- and rocket-propelled-grenade battle in Kabul’s embassy district a little more than two weeks ago.

The agreement between Mr. Obama and Mr. Karzai allows the U.S. military continued access to Afghanistan after a significant drawdown in 2014 and a handover of control for the country’s security to Afghan forces.

Last year, the president withdrew 10,000 troops from Afghanistan and an additional 23,000 are slated to leave by the end of the summer.

After 2014, the U.S. military in the country will be allowed only to train Afghan forces or continue to pursue al Qaeda terrorists. The agreement does not specify the number of troops anticipated in drawdowns leading up to the 2014 transition or afterward.

In his televised remarks, the president said only that reductions “will continue at a steady pace,” and he pledged Afghans will be “fully responsible for the security of the country.”

“We will not build permanent bases in this country, nor will we be patrolling its cities and mountains,” he said. “That will be the job of the Afghan people.”

Mr. Romney did not immediately react to the speech, although several prominent Republicans praised the signing of the Strategic Partnership Agreement.

“This is a day I have been looking forward to for over two years,” said Sen. Lindsey Graham, South Carolina Republican, who serves on the Armed Services Committee. “I am confident that with proper implementation, this will help secure our nation and allies from future attacks using Afghanistan as a staging area.”

But critics on the left, many of whom supported Mr. Obama’s election because of his promise to end the wars in Iraq and Afghanistan during his first term, remained disenchanted after the speech.

“We are pleased to continue to hear President Obama express his support for ending the war in Afghanistan,” said Win Without War Coalition Coordinator Stephen Miles. “The time to bring our troops home is now.”

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