LONDON—The U.K. plans to deploy a navy warship to the Mediterranean to counter arms smuggling in Libya and a team to assist in training the country’s coast guard, Prime Minister David Cameron said Friday, in the latest sign of a step toward military involvement in the country.

Mr. Cameron said leaders of the Group of Seven nations have discussed at a summit in Japan how to tackle migration in the central Mediterranean and boost the capability of the Libyan coast guard.

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