At least 59 bodies have been found on a ranch in Mexico's northern state of Tamaulipas, on the US border, authorities said, warning that the grim toll could rise.

The Tamaulipas state prosecutor's office said 11 people had been arrested and another five kidnapping victims had been set free in the same operation on Wednesday.

Police and military staff learned on March 25 that several buses had disappeared in the area, leading to their investigation which turned up a grisly find: eight mass graves in the La Joya farming village, in the town of San Fernando, the prosecutor's office said.

"With our work that is underway, we are trying to establish if the remains are those of the people who went missing on the buses," the prosecutor's statement said.

Authorities said they feared the number of dead would rise as the remains had only been counted in three of eight mass graves.

The gruesome find was in the same town of San Fernando where 72 migrants from El Salvador, Honduras, Guatemala, Ecuador and Brazil were killed in August 2010 for refusing to work for drug traffickers.

Meanwhile, thousands of outraged citizens took to the streets of 38 Mexican cities, venting anger over widespread violence linked to the country's illegal drug trade.

The protest marches were organised following the murder of a well-known author's son along with four close friends and two others on March 28.

Javier Sicilia, a poet and columnist for the daily La Jornada and the weekly Proceso - two of the country's leading publications - called for the protests following the killing of his son Juan Francisco, 24, near Cuernavaca, 90 kilometres south of Mexico City.

Seven major drug gangs are operating in Mexico whose bloody clashes have left over 34,600 people dead since December 2006, when president Felipe Calderon's government launched a military crackdown that has so far failed to stem the violence.

Authorities said on Saturday that 20 people were killed in less than 24 hours in Ciudad Juarez, which borders the US state of Texas.

Ciudad Juarez is considered the most violent city in Mexico, with more than 3,100 homicides in 2010. Most of the violence is blamed on drug cartels who fight for control of lucrative drug routes into the United States.

On Monday the United States boosted security at its consulate in Mexico's drug war-rocked northern city of Monterrey, where it built a second protective ring wall.

Two other US consulates on the Mexican side of the shared border were temporarily closed last year.

Security concerns forced the office in Ciudad Juarez to close for several days, while another in Nuevo Laredo was closed after an explosive device attack.

- AFP