Thousands of people marched in the capital in the latest demonstration over a case that has repulsed the nation and triggered the biggest crisis of President Enrique Pena Nieto's administration.
The violent protests came a day after authorities said suspected gang hitmen confessed to killing the 43 students and incinerating their bodies in the southern state of Guerrero.
A small group of protesters used metal barricades as battering rams in an attempt to break open the National Palace door.
They briefly set the door on fire and spray-painted the words "we want them back alive" on the 16th-century building.
Pena Nieto uses the palace for ceremonies but he lives in the Los Pinos residence in another part of the capital.
Protesters loudly counted from one to 43 and held candles during the evening march. Some chanted "Pena Nieto out!" and "the people don't want you!"
Hours earlier in Guerrero's capital Chilpancingo, more than 300 students threw rocks and firebombs at the regional government headquarters.
They also burned around 10 vehicles, including trucks and a federal police vehicle, and chanted "they took them alive, we want them back alive" outside the building, which was partially torched in a protest over the case last month.
Gang-linked police attacked busloads of students in the Guerrero city of Iguala on September 26, in a night of violence that left six people dead and the 43 missing.
Attorney General Jesus Murillo Karam said Friday that three Guerreros Unidos gang members confessed to receiving the students from the police before killing them.
The confessions appeared to bring a tragic end to the mystery.
But relatives of the missing and fellow students at their teacher-training college near Chilpancingo refuse to believe the authorities until they get DNA results from independent Argentine forensic experts.
"It appears that the federal government, with great irresponsibility, is interested in closing this matter because it's all based on testimony. There is nothing definitive," said Meliton Ortega, uncle of a missing student.
'Tired' of fear
The students had traveled to Iguala to raise funds but hijacked four buses to return home, a common practice among the young men from a school known as a bastion of left-wing activism.
Prosecutors say the city's mayor, worried that they would interrupt a speech by his wife, ordered the police to confront them. The officers shot at several buses, leaving three students and three bystanders dead.
Authorities have arrested 74 people, including the ousted mayor, Jose Luis Abarca, his wife Maria de los Angeles Pineda, 36 police officers and several Guerreros Unidos operatives.
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.
Demonstrators hold a banner with the pictures of the 43 missing students during a demonstration in Mexico City on Nov 8, demanding justice from the Mexican government in the massacre of 43 missing students. Mexico was confronted with one of the grisliest massacres in years of drug violence after gang suspects confessed to slaughtering the students and dumping their charred remains in a river. - AFP Photo/Omar Torres
The Iguala case has undermined Pena Nieto's assurances that authorities were finally reducing the cycle of murders plaguing the country.
Mexicans fed up with the unrelenting violence rallied behind the Twitter trending topic #YaMeCanse, or #IAmTired, after Murillo Karam was heard uttering the words at the end of his hour-long press conference on Friday.
Protesters spray-painted #IamTiredOfFear on the attorney general's office late Friday.
Parents await DNA tests
Murillo Karam stopped short of declaring all the students dead, and said an Austrian university would help identify the remains. But he warned that evidence indicated it was them.
Parents of the missing say they will not accept they are dead until independent Argentine forensic experts deliver DNA results.
Last month, two hitmen had already confessed to killing 17 of the students and dumping them in a mass grave near Iguala. But officials later said none of the students were among the bodies.
"It hurts to imagine that what they are saying is true," said a mother of a student named Antonio, who like many, refused to give her name.
Despite the unrest, Pena Nieto plans to leave Sunday to attend major summits in China and Australia on a trip that has been shortened due to the crisis.
