A Mexican priest was found murdered in the central state of Michoacan, the state attorney general said on Sunday, the third to be killed in the country in less than a week.

The priest, identified as Jose Alfredo Lopez Guillen, was found on a highway between Puruandiro and Zinaparo.

He had been reported missing last Monday, abducted from his church in rural Janamuato. The kidnapping came after two priests, Fathers Alejo Nabor Jimenez Juarez and Jose Alfredo Suarez de la Cruz, were kidnapped and killed in the Gulf coast state of Veracruz. They were also found dead on a roadside.

Cardinal Alberto Suarez Inda, head of the Morelia archdiocese, said in an online video statement then: "After sharing the enormous pain of the death of two young priests in the diocese of Papantla, Veracruz, we are now suffering our own anguish with the disappearance of one of our priests."

He said that Father Guillen was "a good man, a man who does good, a peaceful man, and so this barbarity is in no way justified".

Autopsy results, which revealed gunshot wounds to be the cause of death, suggested Guillen was killed five days before his body was found..

The murder comes after a decade of drug violence in Mexico that has frequently touched the Roman Catholic Church, with 31 priests killed between 2005 and 2015, according to Christian Solidarity Worldwide.

On Sunday, the state attorney general's office said no ransom calls had been made after Lopez was reported missing earlier in the week. His body was identified by relatives.

Mexico is a strongly Catholic country, with 83 per cent of its citizens identifying as Catholics. However, the Church's vocal opposition to illegal drug trade has made its priests frequent targets for attack.

Mexico's Catholic Multimedia Centre has reported that 520 priests were victims of extortion last year.

Additional reporting by Reuters.