Mexico City's police chief has resigned following sharp criticism of his handling of recent protests against the apparent massacre of 43 college students.

Police chief Jesus Rodriguez Almeida stepped down with immediate effect on Friday, the city's Mayor Miguel Angel Mancera said.

"Today I've received the resignation of the Public Security Secretary [police chief] of this capital," Mancera told reporters on Friday.

The disappearance of 43 young men has ignited weeks of protests, with tens of thousands of people rallying in Mexico City and other regions across the country demanding the authorities find them.

Recent demonstrations have turned violent, with protesters clashing with police and torching government buildings.

One of the biggest marches was staged on November 20, which was peaceful until a confrontation broke out between a small number of people and police.

Most of the arrested protesters have been freed due to lack of evidence, with rights groups accusing the police of indiscriminate violence against activists, journalists and bystanders.

In the hunt for the missing students, authorities have arrested scores of people, including the ousted mayor of Iguala, Jose Luis Abarca, his wife Maria de los Angeles Pineda, dozens of police officers and several Guerreros Unidos operatives.

The Mexican government has said members of the Guerreros Unidos drug gang in the southern state of Guerrero, killed and incinerated the students after police in the town of Iguala intercepted them on the mayor's orders.

In taped confessions, the suspects said they bundled the 43 in the back of two trucks, took them to a nearby landfill, killed them and used fuel, wood, tyres and plastic to burn their bodies for 14 hours.

The victims families have rejected the account in an aim to keep pressure on the government to find the students.