MEXICO CITY—Mexican President Enrique Peña Nieto on Thursday said he would ask the country’s congress to decriminalize personal possession of up to an ounce of marijuana, legalize its medical use and shift public policy from prohibition to prevention of the drug’s consumption.

The proposal comes five months after Mexico’s Supreme Court ruled in favor of four plaintiffs’ right to grow and consume marijuana for personal use. Following the ruling, Mr. Peña Nieto ordered a series of public forums held across the country to gauge...