MEXICO CITY — One of President Enrique Peña Nieto’s signature efforts to shake up the country — a broad plan to overhaul the education system — has run into violent protests that underscore how difficult it may be to carry out, particularly in some volatile states with poor academic performance.

Armed with iron rods and rocks, dozens of masked members of the teachers’ union in Guerrero State attacked the local offices of the four major political parties on Wednesday, smashing windows and overturning furniture. They also set fire to the office of the Institutional Revolutionary Party, or PRI, to which Mr. Peña Nieto belongs.

On Thursday, in a further sign of the growing conflict over education changes, teachers marched down Mexico City’s main boulevard, temporarily closing it down.

The education overhaul, which transfers power from the potent teachers’ union to the federal government, proposes periodic teacher evaluations to determine appointments, salaries and dismissals — a major adjustment for workers who are accustomed to buying or inheriting their positions and who have had, until now, virtual immunity from the state.

The president’s plan, signed into law in February, and the subsequent arrest of the seemingly untouchable boss of the teachers’ union, Elba Esther Gordillo, were seen as political victories for Mr. Peña Nieto, whose agenda is focused on retooling the country’s education, labor, energy and telecommunication sectors.

But additional legislation is needed to carry out the new education law, and dissenting teachers are trying to influence it through a mix of paralyzing protests and vandalism in parts of the country.

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