Buoyant after meeting with the assault force that killed the world's most wanted terrorist, President Obama declared to a hangar full of cheering soldiers Friday that Osama bin Laden's death was proof the U.S. was making progress in Afghanistan and against the global militant group.

"We have cut off their head," Obama said, "and we will ultimately defeat them."

The declaration drew thunderous applause from the 2,300 soldiers, most from the 101^st Airborne Division based at Ft. Campbell, who gathered to hear the president and pay tribute to comrades in the raid.

Obama, meeting with the special operations team members, presented them with the highest honor that can be given to a unit, a Presidential Unit Citation, in recognition of their achievement.

Obama said he was sticking with his plan to begin withdrawing troops from Afghanistan this summer, gradually and in consultation with military leaders. But he seemed to shrug off questions about whether U.S. troops need to remain there.

"Our strategy is working, and there is no greater evidence of that than justice finally being delivered to Osama bin Laden," Obama said during his address at Ft. Campbell.

The meeting with the special operations force was carefully shielded from public view. Adm. William H. McRaven, who ran the Bin Laden operation for the military's Joint Special Operations Command, met Obama at Ft. Campbell's airfield in the afternoon, and the two then went into a closed meeting with a group the White House described as "the full assault force that carried out the operation."

Also at the meeting with Obama and Vice President Joe Biden was the 160th Special Operations Aviation Regiment — a helicopter team known as the Night Stalkers — and the 5th Special Forces Group. Both are based at Ft. Campbell.

The special operations force members did not attend Obama's address, officials said, but were spirited quietly off the base.

Despite the secrecy, it appeared to be Obama's most celebratory public moment yet after this week's raid.

Obama kept his visit with survivors and victims of the Sept. 11, 2001, attacks private when he went to New York a day earlier. And during a Friday visit to a plant in Indianapolis, Obama spoke exclusively about economic issues.

But Obama and Biden, in a victory lap through the "Night Stalkers'" home base, were clearly accepting credit for Bin Laden's long-awaited capture and death.

In a recorded interview to air Sunday on the CBS news program "60 Minutes," Obama said that he wanted to resist the urge to "spike the football" in celebration.

Those strictures were loosened a little on Friday. In his introductory speech, Biden at one point pumped his fist and praised Obama's decision to order the raid on Bin Laden's compound.

Defense Secretary Robert M. Gates did not attend Friday's meeting. He met a day earlier at an "undisclosed location" with members of the special operations team that raided the compound where Bin Laden was killed.

Gates "wanted to personally and privately express his admiration and appreciation for their extraordinary service and historic achievement," Pentagon Press Secretary Geoff S. Morrell said.

At times, military receptions for Obama have been tepid. Even Friday, some at the base said he should have visited earlier. But the president was warmly received. Soldiers interrupted his remarks with cheers and applause, and many crowded the rope line afterward in hopes of shaking hands with the commander in chief.

"This is monumental to me," said Kingston McCaden, a staff sergeant in the transportation battalion. "He's rallying the troops, like in the old days, coming to see us and the Night Stalkers, like the ones who flew in to do the job. I feel really deeply proud."

The Night Stalkers was the regiment that piloted the helicopter mission in Somalia memorialized in the film "Black Hawk Down," according to base public affairs officer Bob Jenkins.

In Sunday's raid, the helicopter pilots averted tragedy. Despite a mechanical failure, they managed to lower the SEALs into the compound housing Bin Laden while they called for backup.

"They're America's quiet professionals," Obama said, calling it one of the greatest military operations in U.S. history. "Their success demands secrecy.… When I gave the order, they were ready."

cparsons@latimes.com

Staff writer David S. Cloud in Washington contributed to this report.