Mexico City — WHEN the Mexican Army actually allows journalists to watch its soldiers in action, it’s often to see them burning marijuana crops. It’s strictly for show, but it’s fun. You get to fly in a military helicopter over the Sierra Madre, then touch down to see troops posing with their rifles as they walk into green marijuana fields. And the highlight: You watch hundreds of pounds of grass go up in flames.

Mexican soldiers have been conducting this ritual for decades, and the photos have come to define the country’s war on drugs. But amid a wave of drug policy reform, those photos may soon disappear from news pages and be relegated to historical archives.

Speaking last month at the United Nations special session on drugs, President Enrique Peña Nieto said he wanted to relax the nation’s marijuana laws. He has since sent Mexico’s Congress a bill to legalize medicine that contains cannabis, allow people to carry an ounce of marijuana without being prosecuted, and free some prisoners convicted on marijuana charges. “We Mexicans know all too well the range and the defects of prohibitionist and punitive policies, and of the so-called war on drugs that has prevailed for 40 years,” he said.

Mr. Peña Nieto is new to the drug-reform game. Only last year, he said he was against legalizing marijuana, and at one point said he was not even going to attend the United Nations session.