A Mexican Catholic priest was killed on Sunday in the southern state of Chiapas after officiating a mass, his religious order and authorities said, marking the latest death in a recent wave of violence in the area.

Marcelo Perez - who was Tzotzil, an Indigenous Maya group native to the area - was leaving the neighbourhood of Cuxtitali in San Cristobal de las Casas, one of the state's largest cities, and returning to his home church nearby when he was killed, the Jesuits in Mexico said in a statement.

Two people on a motorcycle came up to his car, a white Ford, and shot him, according to state prosecutors.

Mexico has seen a streak of murders in the past few weeks, including the beheading of the mayor of the state capital of Guerrero and an intra-cartel war in Sinaloa, which has left hundreds dead or missing, bringing calls for newly inaugurated President Claudia Sheinbaum to take swift action to stamp out crime.

Sheinbaum earlier this month rolled out a four-pronged approach that will also focus on treating the economic and social causes of crime and improving coordination between crime-fighting institutions.

"Father Marcelo has been a symbol of resistance and has stood alongside the communities of Chiapas for decades, defending the dignity and rights of the people and working toward true peace," the Jesuits said.

His death comes as violence has ratcheted up in Chiapas in recent years. From January to August, the state logged around 500 murders, up from 309 in the same period last year, according to official data.

Perez's community said that he had actively spoken out against organized crime in the area.

"Several national and international organizations had publicly warned about the growing number of threats, attacks and acts of criminalization against (Perez), which have intensified in recent years due to his tireless work in favor of justice and the rights of indigenous peoples," the UN human rights office in Mexico said.

"This region doesn't just suffer from murders, but also forced recruitment (into criminal groups), kidnappings, threats and ransacking of its natural resources," the Jesuits said.

Criminal groups have also expanded into trafficking migrants through the state, which borders Guatemala.

Earlier this month, soldiers fired on a convoy they said they mistook for members of a criminal group. The truck was carrying a group of migrants, and six were killed.