The body of Martin Xavier Vazhachira, belonging to the CMI Congregation, who had gone missing, was found on a beach in Edinburgh yesterday, as per a message received by the CMI Church in Thiruvananthapuram.
In a letter to External Affairs Minister Sushma Swaraj, Mr Vijayan sought an investigation into the death citing concerns of the priest's family.
Mr Vijayan said the priest, hailing from Pulinkunnu in Alappuzha district of Kerala, had gone to Edinburgh for higher studies last year.
He had served at St John the Baptist Church, Corstorphine in Edinburgh.
The chief minister also asked Ms Swaraj to take steps to bring the body of the priest to the state as early as possible.
He said the church and relatives of the priest were anxious over the incident.
The role of terror outfits in the case was also being discussed on social media.
In these circumstances, the Indian High Commissioner in London should be directed to arrange for a probe to find out the truth behind the death, Mr Vijayan added.