MEXICO CITY—Mexican President Andrés Manuel López Obrador wants to take the security aid his country receives from the U.S. and use the money instead for a development plan for Central America and southern Mexico to help stop migration.

Mr. López Obrador, a leftist nationalist, took office in December with a plan to fight Mexico’s soaring murder rate by promoting economic development rather than by taking down drug lords. Mexico had a record number of homicides last year—many linked to organized crime—and murders are up again...