MEXICO CITY—President Enrique Peña Nieto, facing the biggest crisis in his first two years in office, proposed a series of measures to confront lawlessness, starting with a cleanup of local police by putting them under the control of state governments.

The initiative to improve Mexico’s law enforcement and rampant corruption comes in response to public outrage over the abduction and suspected massacre of 43 college students who were detained by municipal police in the southern town of Iguala two months ago. Authorities said...