Some 45 African and Western nations and groups in Brussels push peacekeepers in Mali for the medium term, subject to 'appropriate mandate.'
France's initial aim was to block the advance until a UN-authorized African force could deploy to take over the fight.
But the rapid progress of French and Malian forces in ousting the rebels from major northern Malian towns has led some countries to float the idea of moving immediately or in the medium-term to a UN peacekeeping operation.
"There is support shared by the African Union, by France, by the United States, by ECOWAS [a grouping of West African states], all the key players, to gradually move towards a peacekeeping operation under UN control, but in the medium term," French Development Minister Pascal Canfin told reporters during an international meeting on Mali in Brussels.
The French minister said that first, however, the African force must deploy in Mali, as previously agreed. After that, work could take place on converting the African force into a UN peacekeeping operation, provided there is agreement on its mandate.
Diplomats in New York said last week that the UN Security Council would soon begin discussing a possible UN peacekeeping force for Mali, an idea the world body had been uncomfortable with before France's military intervention.
Delegations from around 45 governments and international organisations met in Brussels to discuss ways to reinforce military gains against Islamist rebels in northern Mali by supporting democracy, economic development and human rights in one of the world's poorest countries.
ECOWAS president Kadre Desire Ouedraogo said the grouping, and other African Union countries, want the UN to be involved in follow-up operations in Mali.
Delegates had discussed "eventually" converting the African mission into a UN force, "but with an appropriate mandate so it can act in an effective way to bring peace and security to that zone," he told a news conference.
Chad's Foreign Minister Moussa Faki Mahamat said strong action was needed in Mali to defeat the rebels militarily.
"Afterwards I think a process in the framework of a mission of the United Nations would be opportune," he said.
Mali's Foreign Minister Tieman Coulibaly said he was not against the idea of transforming the African force into a UN peacekeeping force but said it must have a clear mandate.
Some delegates said the advantage of having a formal UN peacekeeping force in Mali was that all UN members are obliged to contribute to its running costs, whereas the African force relies on voluntary contributions.
United Nations Under-Secretary-General for Political Affairs Jeffrey Feltman said the UN was exploring a possible rapid deployment of a mobile team of human rights observers to Mali.
Human rights groups say the French-led offensive in Mali has led to ethnic reprisals by Malian troops.
European Union countries pledged to contribute all but a few dozen of the approximately 500 trainers and soldiers needed for the mission, an EU source said, with France and Germany announcing the biggest new contributions.
"Most of the needs have been filled. We hope that the last posts will be filled in the coming days," the source said, adding that an advance team is expected to leave for Bamako on Friday.
(Editing by Robin Pomeroy)