Obama pressed Libya's veteran strongman Moamer Qadhafi, who has refused to surrender, to "explicitly" give up power and warned exuberant rebels that their struggles were "not over yet."
Looking beyond Qadhafi's iron-fisted reign, he vowed that Washington will be "a friend and a partner" and urged "an inclusive transition that leads to a democratic Libya."
"The situation is still very fluid. There remains a degree of uncertainty, and there are still regime elements who pose a threat," Obama warned in a hastily arranged public appearance on as he vacationed at Martha's Vineyard.
The White House, meanwhile, said it had "no evidence" that Qadhafi had left Tripoli. "The best information that we have," spokesman Josh Earnest told reporters. "There's no evidence to indicate that he's left."
World leaders hailed the rebels' dramatic rout on Sunday of loyalist forces in Tripoli, as Libyans around the world celebrated his imminent downfall.
He thanked NATO for its military support, while cautioning that "the real moment of victory is when Qadhafi is captured" and acknowledged the whole of Tripoli was not under rebel control.
Rebel military spokesman Mohammed Zawiwa told AFP the rebels seized control Monday of the state broadcaster in Tripoli.
"All the television stations controlled by the state have stopped transmitting (in Tripoli). Our fighters have gone in and taken control of the facilities," Zawiwa said.
Elsewhere in Tripoli, rebel fighters packed in trucks, cars and pickups streamed during the day from liberated areas of western Libya towards the symbolic Green Square in the heart of the city, brandishing arms.
Many of the rebels were waving flags of the revolution as they appeared to be heading to the square and then onwards to join rebels trying to snuff out the last pockets of resistance, especially outside Qadhafi's Bab al-Azizya compound in Tripoli.
"The area around Al-Azizya is still a hot spot. There are forces that continue to fight the rebels. He (Qadhafi) could still be in Al-Azizya, or in neighbouring areas," he said.
Foreign correspondents based in the capital's Rixos hotel, separated by a wooded area from Qadhafi's residence, said the atmosphere was tense late on Monday but without reporting any major confrontation.
Qadhafi broadcast three defiant audio messages on Sunday, vowing he would not surrender and urging the people of Tripoli to "purge the capital," even as rebel forces swept through the capital and took over waterfront Green Square.
But he has not been seen in public for weeks.
Hundreds of jubilant Libyans meanwhile converged on their embassies and consulates in Europe and elsewhere to raise the rebel flag and tear down the symbols of Qadhafi's 42-year rule.
Some of the Libyan Arab Jamahiriya's diplomats announced they were defecting to the rebel administration while others deserted their representations.
France welcomed the apparent defeat of Qadhafi's regime and said it would host a summit of the international "Contact Group" coordinating a response to the conflict.
Diplomats from the Contact Group will first meet on Thursday "to coordinate next steps," the US State Department said.
In London, British Prime Minister David Cameron said Qadhafi's regime was in "full retreat" and he should give up any hope he has of clinging on to AFP
Thousands of residents poured onto the streets of Tripoli Sunday night to welcome the rebels, congregating at Green Square, which they renamed Martyrs Square.
Many waved the red, black and green flag of anti-regime forces, dancing in joy and shouting Allahu Akbar (God is greatest). Some fired rifles into the air.
Similar scenes of jubilation were witnessed in Benghazi, the rebels' bastion in the east, where tens of thousands of delirious residents danced and proclaimed the end of the regime of the "tyrant" Qadhafi.
UN leader Ban Ki-moon said the heads of the African Union, European Union, Arab League and other regional groups would attend a summit on Libya later this week in New York.
"The United Nations is now prepared to assist in all vital areas" including security, rule of law, economic recovery, writing a constitution and holding elections, Ban told reporters.
The International Criminal Court, meanwhile, is seeking the transfer of Qadhafi's captured son Seif al-Islam to The Hague to face charges of crimes against humanity, the court's spokesman said Monday.
"The court as a whole is involved," Fadi El-Abdallah told AFP, answering 'yes' when asked if that meant discussions were underway with the Libyan rebel National Transitional Council (NTC) over Seif al-Islam's transfer.
The International Organisation for Migration (IOM), meanwhile, said that it had dispatched a ship with a capacity to carry 300 people to Tripoli to evacuate migrants.
"The boat, the Tasucu, is due to arrive in Tripoli on Tuesday and will leave for Benghazi as soon as IOM is able to successfully board the migrants," said the inter-governmental agency.
Meanwhile Brent oil sank Monday on the prospects of a recovery in Libyan crude output as the rebels advanced deep into Tripoli.
Copyright AFP (Agence France-Presse), 2011