MEXICO CITY—President Enrique Peña Nieto and his national-security team signaled a new tack Monday in Mexico's drug war, blasting their predecessors' policies while offering new measures like a rural gendarmerie to try to take back territories out of government control.

The speeches, the first by the new administration on tackling crime, were notable as much for their tone as their substance: In his address, Mr. Peña Nieto mentioned neither drugs nor drug traffickers, instead...