* UN Security Council expected to start discussing idea
* Meeting looks at boosting Mali politically, economically (Adds quotes, meeting under way)
African and Western countries threw their support on Tuesday behind the idea of having United Nations peacekeepers eventually take over from an African force being deployed in Mali.
France sent troops to Mali last month to halt the advance of al Qaeda-affiliated militants who launched an offensive that threatened the capital Bamako.
France's initial aim was to block the advance until a U.N-authorised 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 U.N. peacekeeping operation.
"There is support shared by the African Union, by France, by the United States, by (West African grouping) ECOWAS, all the key players, to gradually move towards a peacekeeping operation under U.N. control, but in the medium term," French Development Minister Pascal Canfin told reporters during an international meeting on Mali in Brussels.
But he said the African force must first deploy in Mali, as agreed. After that, work could take place on converting the African force into a U.N. peacekeeping operation although there would have to be agreement on its mandate.
Diplomats in New York said last week that the U.N. Security Council would soon begin discussing a possible U.N. 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 ECOWAS and African Union countries wanted the United Nations to be involved in follow-up operations in Mali.
Delegates had discussed "eventually" converting the African mission into a U.N. 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 U.N. peacekeeping force but said it must have a clear mandate.
Some delegates said the advantage of having a formal U.N. peacekeeping force in Mali was that all U.N. 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 U.N. 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.