Diplomats here said it gave him leverage in keeping African and European leaders listening and their doors open. If Libya sent all the migrants home, they would become a burden to poorer African nations, which would have to absorb them while losing out on the remittances they send home. At the same time, diplomats here said, Libya has made it plain to European countries, especially Italy, that if Libya chose to look the other way, most of those migrants would head for European shores. “It’s a kind of soft power they use,” said one Western diplomat who works on Libyan affairs but requested anonymity for fear of antagonizing Libyan authorities.