Tripoli.- As rebels fought a desperate battle with die-hard regime loyalists for control of the Libyan capital Tripoli, governments around the world urged strongman Muammar Gaddafi to end the bloodshed and surrender.

US President Barack Obama led the calls for Gaddafi to relinquish power after six months of rebellion and NATO bombings culminated in a lightning rebel advance into the heart of Tripoli over the weekend.

"The surest way for the bloodshed to end is simple: Muammar Gaddafi and his regime need to recognize that their rule has come to an end," Obama said in a statement, according to Reuters.

"Gaddafi needs to acknowledge the reality that he no longer controls Libya. He needs to relinquish power once and for all."

French President Nicolas Sarkozy praised the bravery of the rebels and promised them the continuing support of the French government, one of the main instigators of the NATO intervention in Libya under a UN mandate to protect civilians.

"At the moment when decisive events are taking place in the Tripoli region, in Tripoli itself, and elsewhere in Libya, the president salutes the courage of the rebel fighters and of the Libyan people who are rising up," Sarkozy's office said, Reuters reported.

"He assures them once more of the full support of France to achieve the liberation of their country from oppression and dictatorship."

British Prime Minister David Cameron, another staunch backer of the NATO air campaign which helped the rag-tag rebel forces by destroying Gaddafi's military assets, cut short a break in Cornwall to attend a National Security Council meeting in London.

"It is clear from the scenes we are witnessing in Tripoli that the end is near for Gaddafi," a statement from his Downing Street office said, according to AFP.

"He has committed appalling crimes against the people of Libya and he must go now to avoid any further suffering for his own people."

The European Union said it was planning for a post-Gaddafi Libya and urged the colonel to leave "without further delay."

"We seem to be witnessing the last moments of the Gaddafi regime and we call on Gaddafi to step down without further delay and avoid further bloodshed," EU foreign affairs spokesman Michael Mann said, as reported by Reuters.

NATO Secretary General Anders Fogh Rasmussen said Gaddafi's regime was crumbling and his defeat was only a matter of time.

"The sooner Gaddafi realizes that he cannot win the battle against his own people, the better - so that the Libyan people can be spared further bloodshed and suffering," he said, according to Al Jazeera.

Gaddafi's whereabouts were unknown but loyalist forces including tanks and snipers are continuing to battle rebels in pockets of the capital, according to various media reports.

Even as rebels swarmed into Tripoli on Sunday and were met by jubilant residents, the defiant colonel broadcast messages telling his forces to crush the "rats" and traitors.