(Adds details, background)

By Steve Scherer

ROME Dec 2 (Reuters) - Italy wants to host an international meeting in Rome this month to promote a political deal between rival governments in Libya and open the way to fight Islamic State militants there, the Foreign Minister said on Wednesday.

A war between the two governments and their armed factions for control of Libya has allowed Islamic State militants to gain a foothold there, raising fears among governments in the region that the group could stage more attacks further afield.

Militants, some of whom trained in Libya, carried out two major attacks targeting tourists in neighbouring Tunisia this year. Islamic State also claimed a suicide bombing last week that killed 12 members of Tunisia's presidential guard.

European governments worry Islamic State militants could slip across the Mediterranean among a stream of refugees heading for Europe.

"Italy is at work to bring the international community together to make a decisive push" for a political agreement on a unity government in Libya, Foreign Minister Paolo Gentiloni said in the Senate.

The proposed date for the meeting, which would include governments from the region and the "main global players", is Dec. 13, Gentiloni said. He said it was urgent to get an accord in place quickly in order to fight Islamic State, or Daesh.

"The fact is we don't have much time, and we don't want to give time to Daesh," he said.

Late on Tuesday, the new United Nations envoy, Martin Kobler, told Reuters Libya's warring factions are very close to a deal on forming a unity government and could sign an accord in a month. Talks have been going on for about a year.

Islamic State in Libya has between 2,000 and 3,000 fighters and is the only affiliate known to have received support and guidance from the extremist group's stronghold in Syria and Iraq, U.N. experts said in a report circulated on Tuesday.

Last week, Italian Prime Minister Matteo Renzi and French President Francois Hollande said world powers need to step up efforts to stop Islamic State gaining ground in Libya.

The U.N. report also said Islamic State is struggling to expand its territory in Libya because it lacks fighters, and the militant group is having a hard time winning local support because it is viewed as an "outsider." (Editing by Raissa Kasolowsky)