Gunmen in Mexico have shot dead a Catholic priest who was an outspoken advocate for indigenous rights and who had condemned the violence plaguing his community.

Father Marcelo Pérez was killed after celebrating Mass in the southern state of Chiapas on Sunday, the prosecutor's office said.

The Jesuit priest had spent almost two decades fighting for the rights of the Tzotzil indigenous group, of which he was a member.

The Jesuit Order said his murder should not be "minimised" as an isolated case - insisting it was part of the wave of violence that organised crime groups have unleashed in Chiapas.

"Father Marcelo has been a symbol of resistance and support in Chiapas, defencing the dignity, the rights of the people, and the construction of an authentic peace," the Jesuit Order said.

Mexican President Claudia Sheinbaum said his murder was being investigated and would not go unpunished.

Mexico's bishops' conference described Father Marcelo as one of the "prophetic voices" that had fought for peace, and said justice in Chiapas had been silenced.

The priest was killed by two men on a motorcycle, who opened fire on his vehicle in the city of San Cristóbal de Las Casas.

The incident happened early on Sunday as Father Marcelo was returning to his parish after saying Mass in the Cuxtitali neighbourhood of the city.

He had been transferred to San Cristóbal de Las Casas after receiving death threats in the rural parish where he had previously worked.

The priest had tried to negotiate an end to the violence caused by clashes between a criminal gang and a vigilante group.

In an interview last month, he had described the southern state of Chiapas as "a time bomb".

"There are many [people who have] disappeared, many who have been kidnapped, many who have been murdered because of the presence of organised crime here," he said as he was leading a protest march he described as a "pilgrimage".

Chiapas has seen a spike in violence over the past year, with the Sinaloa cartel and the Jalisco New Generation Cartel fighting for control of the area.

The criminal groups extort migrants who cross the southern state on their way north to Mexico's border with the United States.

Communities in the region have been hard hit by the violence, sometimes having to hide in their homes for days as shots ring out outside.

But the targeted murder of an outspoken human rights advocate is seen as a dangerous escalation of the violence that has been plaguing the community for months.