Rebels, Western Leaders Meet to Map Libya's Future
Members of Libya's caretaker rebel government, the National Transitional Council (NTC), are at the meeting, hosted by French President Nicolas Sarkozy, British Prime Minister David Cameron, and US Secretary of State Hillary Clinton.
Earlier in the week, Qaddafi's wife, two of his sons and his daughter fled to neighboring Algeria.
And Algerian media reported that Qaddafi had also tried to seek refuge there.
According to a report in El Watan newspaper, the colonel tried to speak to Algerian President Abdelaziz Bouteflika from the desert town of Ghadamis, just on the Libyan side of the border, but the Algerian leader refused to take the telephone call.
The fugitive strongman remains at large - while his sons Saif al-Islam and Saadi are encircled in Sirte - but world leaders and the NTC are already planning for a Libya without the iconic and eccentric Qaddafi clan.
Delegates at the Paris meeting are expected to discuss plans for the transition to democracy, for reconstruction and issues such as enhancing the training of police.
The NTC is expected to press for a further unfreezing of assets, but its delegates will also stress that it does not want any lessening of NATO support as it tries to quell the remaining loyalist pockets.
The EU announced on Thursday that it had lifted sanctions on 28 entities - including oil firms and port authorities - to help the NTC get the economy moving again. The decision will take effect on Friday.
The UK, US and France have unfrozen more than $5bn in Libyan assets this week, and other countries are making similar moves.
On the diplomatic front, Russia is the latest nation to agree to recognize the NTC as Libya's legitimate government.
About 60 countries are attending the "Friends of Libya" forum in Paris on Thursday afternoon, along with UN Secretary-General Ban Ki-moon.
The meeting comes on the 42nd anniversary of Qaddafi's emergence as the leader of the coup that overthrew King Idris - whose grandson some Libyans want to restore.
But with so much international money and influence on the table many ask just who the NTC is representing – the NATO powers backing them or the Libyan people.