BRUSSELS—Seeking to head off a potential increase of migrant flows from North Africa, European leaders discussed Friday scaling up the bloc’s naval operation to fight people-smuggling gangs off the Libyan coast.

U.K. Prime Minister David Cameron told EU leaders gathered in Brussels Thursday night that he was prepared to extend the mission of Royal Navy vessel HMS Enterprise in the central Mediterranean at least until the summer and wanted to see it deployed in Libyan territorial waters, according to a government official....