They alleged that Bajrang Dal activists attacked the gathering, beat up some of the priests, and torched the theological school's vehicle, and that the police had detained six of the carol singers from Satna.
The Bajrang Dal has direct links with Modi's ruling Hindu-nationalist Bharatiya Janata Party (BJP).
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The mob attacked the Christian students inside the police station, and set fire to the priest's auto parked outside.
"Any form of violence in the name of religion needs to be stopped immediately through a collective and strong political will by the government, both at (the) central and state levels", he said. "We have registered a case against unidentified people who burnt the auto", she said.
On Thursday, on the basis of a complaint lodged by Mr. Dohar, Father M. George and a group of 30 seminarians were detained during the routine carol singing.
Leo Cornelio, the archbishop of Bhopal diocese, described the incident as "repeated shameful acts of the fundamentalists to rise above the law in attacking the Christian brothers who are spreading love, peace and brotherhood".
Denying allegations of conversion, Father Rony had said the Diocese has been running a seminary at Barakala village in Satna district for 20 years and not a single person has been converted to Christianity.
"Our members have registered a criminal case because we have proof to show how Christian priests were forcibly converting poor Hindus", Abhay Kumar Dhar, a senior member of the Bajrang Dal in Bhopal, the capital of Madhya Pradesh, told Reuters.
The police said detention followed claims by one Dharmendra Dohar who alleged he was being forced to "embrace Christianity".
"Except the priest who was arrested others were allowed to go on Friday".
Eight priests who went to inquire about the detained priest and seminarians were also taken into custody.
Local Christians said that representatives from a theological school in Satna town, 15km form the village, had come to lead the carol-singing session as part of pre-Christmas celebrations. "They gave us a Bible and Rs 5000 in cash", he said.