Official figures from Mexico show that the number of homicides was higher by a third in January compared to the same month of 2016.
The authorities believe the spike in violence is linked to the extradition of the drug lord, Joaquin Guzman, known as "El Chapo," or "Shorty".
The former leader of the Sinaloa Cartel was sent to a high security jail in the United States last month.
His departure has prompted a fight for power in northern Mexico states.
The Sinaloa Cartel controls some of the most lucrative drug trafficking routes in Mexico.
The Mexican authorities had predicted a surge in violence following Guzman's extradition and promised to deploy extra troops.
But in the worst-affected areas, including the northern states of Baja California, Chihuahua and Guzman's native Sinaloa, homicides were up by 50% in January.Image copyright EPA Image caption The Mexican government expected a surge in violence once it announced Guzman's extradition
In total, 1,938 people were murdered in Mexico last month, a 34% rise on January 2016, when 1,442 homicides were reported.
Defence Minister Salvador Cienfuegos says the recent violence has been caused by a power struggle among different factions of the Sinaloa Cartel.
Guzman is being held in a maximum security prison in New York after he was extradited last month.
The notorious kingpin escaped twice from prison in Mexico, once in a laundry basket and most recently through a tunnel in his cell.
He appeared in court last month and pleaded not guilty to charges that he ran the world's largest drug-trafficking organisation during a decades-long career.
He faces life in prison in the US if convicted.
US Secretary of State Rex Tillerson and Department of Homeland Security Secretary John Kelly are due to meet Mexico's Foreign Secretary, Luis Videgaray, in Mexico City on Thursday.
The talks are expected to focus on migration and the wall the US intends to build along its southern border.
But they are also due to discuss security and ways of curbing the power of Mexico's drug trafficking gangs.