PARIS - World leaders on Monday hailed the rebel takeover of Tripoli, urging Moammar Gaddafi to admit defeat, as Libyans around the globe celebrated the veteran strongman's imminent demise.

The dramatic push to wrest full control of the Libyan capital from Gaddafi loyalists was seen as the end-game in the six-month uprising against his 42-year rule.

"The Libya that you deserve is within your reach," US President Barack Obama said in a message to Libya's insurgents, cautioning "there will be huge challenges ahead."

Obama vowed that Washington will be "a friend and a partner" in the country's future and urged "an inclusive transition that leads to a democratic Libya."

As the leaders who supported the uprising stressed that Libya's fate should be decided by Libyans, they piled pressure on one of the planet's longest-standing dictators.

"Although it's clear that Gaddafi's rule is over, he still has the opportunity to reduce further bloodshed by explicitly relinquishing power," Obama said in a hastily arranged public appearance as he vacationed on the resort island of Martha's Vineyard.

Announcing a special Libya summit with the heads of the European Union, Arab League and African Union this week in New York, UN Secretary General Ban Ki-moon called on Gaddafi's fighters to "cease violence immediately and make way for a smooth transition."

"This is a hopeful moment, but there are risks ahead," Ban said.

French President Nicolas Sarkozy, whose country spearheaded support for the rebels and was the first to recognize their administration, condemned Gaddafi's "irresponsible and desperate calls for the combat to continue."

Sarkozy urged "forces still loyal to the regime to turn away from the criminal and cynical blindness of their leader, to cease fire."

Sarkozy's office said he had invited the prime minister of the rebel National Transitional Council (NTC) to meet him in Paris on Wednesday while France 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.

Spain meanwhile called for the "adoption as quickly as possible of new (UN) resolution" to take into account the latest developments.

Italian Prime Minister Silvio Berlusconi, who signed a 2008 friendship treaty that made the former colonial power Libya's top trading partner, urged Gaddafi to "put an end to every pointless resistance".

German Chancellor Angela Merkel welcomed "the beginning of the breakdown of... Gaddafi's regime" and said the international community needed to move quickly "to enable a transition to a peaceful, free and democratic society because Libyans have suffered too much."

Leading European Union figures also called for Gaddafi to quit.

"We seem to be witnessing the end of the Gaddafi regime," said Michael Mann, spokesman for EU foreign affairs chief Catherine Ashton. "Gaddafi has to relinquish power now and avoid further bloodshed."

Mann also urged the rebel forces to "fully respect humanitarian and human rights law and protect citizens", as they gain control of the country.

The Arab League declared "full solidarity" with the rebels while Libya's neighbor Egypt, where Hosni Mubarak had to quit power following a popular revolt earlier this year, officially recognized their administration.

In Libya's other neighbor Tunisia, whose popular uprising earlier this year launched the Arab Spring protest movements, the foreign ministry hailed "the victory of the Libyan revolution" as a "historic change of great importance."

Morocco officially recognized late Monday the rebels' National Transitional Council (NTC) as the "only legitimate representative" of the Libyan people.

British Prime Minister David Cameron said that "Gaddafi must stop fighting, without conditions, and clearly show that he has given up any claim to control Libya," while Canadian Prime Minister Stephen Harper called on the Libyan people to "now chart their own democratic course."

NATO, whose aerial bombing played a key role in weakening the regime's military infrastructure, urged Gaddafi to give his country a chance to rebuild.

It is "time to create a new Libya -- a state based on freedom, not fear; democracy, not dictatorship; the will of the many, not the whims of a few," alliance head Anders Fogh Rasmussen said.

Hundreds of jubilant Libyans converged on their embassies and consulates in Europe and elsewhere to raise the rebel flag and tear down the symbols of Gaddafi's rule. Diplomatic staff at some embassies also announced they were joining the rebels.

Demonstrators at embassies tore Gaddafi portraits, hauled down his regime's green flag and ripped up copies of his Green Book, the 1975 text in which Gaddafi laid out his philosophy.

Venezuelan President Hugo Chavez, an old Gaddafi ally, was a lone voice of foreign support for the crumbling regime, accusing the West of "destroying Tripoli with their bombs."

China was measured in its reaction and promised to cooperate with whatever government would take over, while Russia urged any future political dialogue in Libya to take place without foreign interference.

Looking to the future, Washington said it was working with international partners on ways to continue financing the NTC, while the World Bank said it would "re-engage with Libya just as soon as we can be helpful in the country's recovery."

The oil market was quick to react, with crude prices sliding on prospects of output in one of Africa's top producers getting fully back on stream and easing pressure on supply to Europe.