Angry protesters tried to break into Mexico City's National Palace late Saturday while others torched several trucks in the southern state of Guerrero, where the students vanished in September.
Thousands of people marched in the capital over a case that has repulsed the nation and triggered the biggest crisis of President Enrique Pena Nieto's administration.
The protests came a day after authorities said suspected Guerreros Unidos gang hitmen confessed to receiving the 43 students from local police, killing them, incinerating their bodies and dumping them in a river in Guerrero.
But the apparent mass murder has shattered Pena Nieto's attempts to move Mexico's narrative away from years of drug violence and toward the economic reforms that has earned him international praise.
Despite the unrest, Pena Nieto left for China to attend an Asia-Pacific Economic Cooperation (APEC) summit before a two-day state visit in the country, with which he has sought closer ties.
He will then travel to Brisbane, Australia, for a G20 summit. The trip ends Saturday.
Amnesty International has criticized his decision to carry on with the trip, saying it "shows the lack of interest in confronting the grave human rights situation in Mexico."
The then handed the students to the Guerreros Unidos.
Prosecutors say the city's mayor, worried that the students would interrupt a speech by his wife, had ordered the police to confront them.
If the confessions are true, the mass murder would rank among the worst massacres in a drug war that has killed more than 80,000 people and left 22,000 others missing since 2006.
In Mexico City, protesters chanted "Pena Nieto out!" and "the people don't want you!"
They tossed Molotov cocktails at the door, which sparked a brief fire, and spray-painted the words "we want them back alive" on the 16th-century building.
Security forces later took back control of the door. Pena Nieto uses the palace for ceremonies and he lives in the Los Pinos residence in another part of the capital.
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