Mexican police have arrested a man accused of murdering a Roman Catholic priest and human rights campaigner in the southern state of Chiapas.

Father Marcelo Pérez was killed on Sunday after celebrating Mass at his church in the city of San Cristóbal de las Casas.

Witnesses say the shots came from two men who approached the church on a motorbike.

The authorities identified the alleged murderer as Edgar N, a local drug dealer.

Father Marcelo had campaigned tirelessly against drug trafficking in Chiapas, which has seen a surge in violence in recent years linked to turf wars between rival cartels.

Mexico's bishops' conference said the murder had silenced a "prophetic voice" who had worked tirelessly for peace and justice.

According to the Chiapas public prosecutor's office, his suspected killer had been identified using security camera footage, witness testimony and other leads, AFP news agency reports.

Father Marcelo had been killed by two men on a motorcycle, who opened fire on his vehicle.

The incident happened early on Sunday as Father Marcelo was returning to his parish after saying Mass in the Cuxtitali neighbourhood of San Cristóbal de Las Casas.

He had been transferred to the city 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 that he described as a "pilgrimage".

Hundreds of mourners attended his funeral on Tuesday in his home town, San Andrés Larráinzar, chanting "Long live Father Marcelo, priest of the poor", AFP reports.

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 exploit 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.