MEXICO CITY — Facing waves of anger and frustration after local officials and the police were implicated in the disappearance and presumed murder of 43 college students, President Enrique Peña Nieto on Thursday proposed a broad plan to revamp local policing, stamp out corruption and establish the rule of law nationwide.

Mr. Peña Nieto delivered a 30-minute, wide-ranging televised address meant to pull himself out of the lowest point of his two-year tenure and respond to mass demonstrations expressing frustration with the political class and demanding action.

The more than 1,800 municipal police forces would effectively be disbanded and come under the control of state governments, and the federal government would have the power to dissolve municipal governments found to be corrupt. The public would have more opportunity to review government contracts. A national 911 system would be installed, and jurisdiction confusion among the nation’s police, which often hampers investigations, would be clarified.

The president also proposed measures to address poverty and the economic disparity between the northern and southern parts of the country, though even affluent states have had serious organized crime problems.