As rebels celebrated in Tripoli, President Barack Obama declared Monday that Moammar Gadhafi’s long rule is over. “The future of Libya is in the hands of its people,” he said.

Speaking from a rented vacation home on Martha’s Vineyard, Obama heralded U.S. and international military efforts that helped bring about the outcome. But with Gadhafi’s precise whereabouts unknown, the president cautioned that uncertainty and threats remained.

Obama called on Gadhafi to surrender and end the bloodshed, and on the opposition to seek a just transition into an uncertain future.

“The rights of all Libyans must be respected,” he said. “True justice will not come from reprisals and violence; it will come from reconciliation and a Libya that allows its citizens to determine their own destiny.”

The crumbling of Gadhafi’s 42-year rule was being described by some analysts as vindication of Obama’s much-criticized decision to limit U.S. involvement in Libya and let NATO take control after the U.S. led the initial air campaign in March.

Obama stopped well short of declaring a military or political victory, leaving it to a spokesman to credit U.S. strategy and “the president’s robust leadership” with producing “a lot of favorable results.” But the president highlighted NATO’s success after months of doubts about whether the alliance would be able to prevail.

“NATO has once more proven that it is the most capable alliance in the world and that its strength comes from both its firepower and the power of our democratic ideals,” he said. 

With his re-election campaign under way and a war-weary public focused on jobs, Obama was quick to note that it all happened “without putting a single U.S. troop on the ground” — a policy aides said Obama would maintain.

It’s come at a cost, though: The Pentagon says that as of June 30, the U.S. had spent about $896 million, including the daily military operations, munitions and humanitarian assistance.

Obama’s comments Monday were his first since a weekend push by the rebels into the Libyan capital, and since he arrived on this island retreat off the coast of Massachusetts on Thursday for a 10-day stay

The White House had defended Obama’s decision to go on vacation during a time of high unemployment by arguing that a president can never really go on vacation. That reality was on display as the developments in Libya came to a boil, and Obama was forced to interrupt his plans for beach time and golf for briefings and statements.

Obama was briefed over the phone Monday by top national security staff, including Secretary of State Hilary Rodham Clinton and Defense Secretary Leon Panetta. Then he donned a suit jacket to speak to reporters in the yard of his rented waterside farm, before heading out to play basketball.

Obama also fit in a call to British Prime Minister David Cameron, as the U.S. and international partners that have recognized the rebel Transitional National Council worked to find a way forward. Clinton telephoned the leader of the Libyan Transitional National Council on Monday.