Thousands marched along Mexico City's main boulevard, chanting for President Enrique Pena Nieto to resign and waving blackened flags of the country in anger over the case of the missing students.
They echoed "you are not alone" to parents of the missing who joined the rally at the Angel of Independence Monument.
"Pena Nieto must resign," Clemente Rodriguez, father of missing student Cristian, told the crowd after two leading newspapers showed the embattled president's approval rating dropping to around 40 per cent.
Hundreds of riot police protecting the Senate used fire extinguishers to repel the protesters.
Around 15 protesters were slightly injured, a Red Cross worker at the scene told AFP.
Three people, including a 17-year-old, were detained over the vandalism, a city government spokesman told AFP.
Pena Nieto, who took office on December 1, 2012, has faced a wave of protests that have ended in sporadic acts of violence since the students vanished two months ago.
A group of protesters ransacked the Guerrero state prosecutor's office in the regional capital, Chilpancingo, and set five vehicles on fire, including two police cruisers.
Families refuse to believe the 43 young men are dead and demand they be found alive. Prosecutors have stopped short of declaring them dead, saying they await DNA tests on charred remains sent to an Austrian university.
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