MEXICO CITY — A day of mostly peaceful antigovernment mass marches on Thursday to protest the disappearance, and presumed murders, of 43 college students ended with clashes with the police who tried to prevent some demonstrators from damaging the National Palace in the city center.

Thousands of people led by relatives of the missing students marched through the city and converged at night at the historic square known as the Zócalo, many of them pleading with masked young people to refrain from violence or stay out of the march.

Demonstrators, mostly students and members of teachers’ unions joined by celebrities, artists and others, focused their ire on President Enrique Peña Nieto, with echoing shouts of “Peña Nieto out!” and an effigy of the president that was burned.

It was one of the largest of the occasionally violent demonstrations that have taken shape since the students, from a left-leaning college with a history of provocative protest, disappeared on Sept. 26 in the town of Iguala, 120 miles south of Mexico City, shocking a country increasingly frustrated with crime and corruption.