President Obama said Monday that Muammar al-Qaddafi's regime is "coming to an end" but the fighting is "not over yet," as Libyan rebels brought Qaddafi's forces to the brink of collapse. 

The president emerged from his vacation in Martha's Vineyard to publicly address the historic developments in Libya, where rebels moved with remarkable speed to capture control of most of Tripoli. 

"The future of Libya is in the hands of its people," Obama said. "The celebrations that we've seen in the streets of Libya shows that the pursuit of human dignity is far stronger than any dictator."

Obama noted that there is still "fierce fighting" in some areas, and urged Qaddafi -- whose location in unknown -- to publicly give up power. 

"Although it's clear that Qaddafi's rule is over, he still has the opportunity to reduce further bloodshed by explicitly relinquishing power to the people of Libya and calling for those forces that continue to fight to lay down their arms for the sake of Libya," Obama said. 

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In addressing the developments, Obama paused to remember all the Americans killed by the regime "in acts of terror in the past." And he touted the combined efforts of the United States and its NATO allies in supporting the anti-Qaddafi rebel movement since March. 

"The Libyan intervention demonstrates what the international community can achieve when we stand together as one," he said. "Although the efforts in Libya are not yet over, 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."

Going forward, Obama said the U.S. and its allies are working to make sure "critical supplies" reach the country. He also said Qaddafi's frozen assets will be used to support the Libyan people. 

Still, Obama administration officials stressed Monday that U.S. military involvement in the country would not be expanding. 

A State Department spokeswoman said this must be a "Libyan-led transition." The Pentagon said the U.S. still does not plan to send forces into Libya. 

"There will not be U.S. boots on the ground," Pentagon spokesman Col. Dave Lapan said. "If there is going to be some type of transitional mission that remains to be seen -- whether it comes out of the U.N. or NATO, but we still do not plan any U.S. forces going onto the ground into Libya." 

But a NATO official told Fox News the multi-national mission in Libya is not expected to end in the coming days -- even if Qaddafi is captured or killed. 

The official said the NATO mission would end only when Qaddafi's forces withdraw to their bases or surrender; attacks against the civilian population cease; and the free flow of humanitarian goods and services is established. 

The official said NATO is still preparing to transfer leadership to the United Nations. If all nations agree, this phase could include sending NATO troops into Libya as part of an effort to observe and stabilize conditions on the ground. Other countries from the Arab League or African Union could also play a part in that security effort. 

The NATO official said it will remain crucial to enforce a no-fly zone and prevent illegal weapons shipments from entering the country. Qaddafi still has some forces in his home town of Sirte as well as in Brega and Sabha, the official said, though many have "lost the will to fight." 

"It's over for him," State Department spokeswoman Victoria Nuland said Monday. 

She also said Secretary of State Hillary Clinton has been "working the phones all morning" to get a handle on the developments in Libya. She said Clinton and the opposition leader "discussed ways that the international community can assist Libyans with the urgent work of protecting civilians and proving key services as well as the TNC's efforts to assemble an inclusive new government to protect the rights and aspirations of all citizens."

Nuland said that while no new funds have yet been released, the U.S. is "trying to accelerate" the release of the Qaddafi regime's frozen assets to the Libyan people. Nuland estimated the value of the assets at $30 billion, with 10 percent of it liquid. 

Fox News' Justin Fishel contributed to this report.