BRUSSELS—The European Union agreed to launch a mission against Libyan migrant-smuggling gangs, though its scope depends on backing from Libya’s fractious authorities and the United Nations Security Council.

The move by EU foreign and defense ministers puts the bloc on course to launch some kind of naval operation as soon as next month. The plans approved by the ministers on Monday calls for the mission to be based in Rome and headed by Italian Rear Adm. Enrico Credendino, EU officials said.

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