French President Nicolas Sarkozy and British Prime Minister David Cameron will jointly host the meeting of the contact group on Libya next week in Paris, said a statement issued Monday night by the Elysee Palace, confirming Foreign Minister Alain Juppe's early remarks on local media.

Both leaders decided after a telephone talk "to initiate without delay a close cooperation with the legitimate Libyan authorities and their international partners for the organization of a summit of the enlarged contact group on Libya next week in Paris," the statement said.

They both agreed to continue their support for Libya's rebel authority -- National Transition Council (NTC) as long as Muammar Gaddafi refused to lay down arms, the statement added.

Shortly before the statement was released, Juppe told local television channel TF1 more about the international contact group's gathering in Paris which he proposed earlier in the day.

The contact group on Libya was formed at an international ministerial conference in London on March 29 and is composed of European powers, the United States, allies from the Middle East and a number of international organisations.

According to Juppe, Gaddafi's regime "is now evidently finished" but "the victory is not complete," so vigilance should be remained.

Sarkozy's office announced around noon that a meeting with NTC leader Mahmoud Jibril in Paris is put on agenda.

The Elysee latest statement added that Sarkozy also had a talk in the night with UN Secretary General Ban Ki-Moon. They estimated that the United Nations, if the legitimate Libyan authorities wish, would have an important role to play to accompany the transition phase that will take place.

Libya rebels reportedly have taken the majority of Tripoli, Libyan capital and the stronghold of pro-Gaddafi troops. But neither the rebels or the NATO coalition force know where Gaddafi himself is hiding as fighting continues.