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Jagtar Singh Johal from Dumbarton, West Dunbartonshire, was detained in Jalandhar in the state of Punjab on November 4.
The Sikh Federation UK said no official charges have yet appeared but local media reported Mr Johal’s arrest was linked to the killing of Hindu leaders in Punjab.
The group said the 30-year-old should be enjoying married life but “finds himself the subject of some sort of conspiracy hatched by the Punjab police and leading politicians”.
Mr Johal, who got married in India in October, has told lawyers he has been tortured with “body separation techniques and electrocution to body parts”.
At a court hearing on Tuesday to extend his remand until the end of the week, Mr Johal’s lawyer requested an independent medical examination of his injuries.
Last week, the Foreign and Commonwealth Office said it was in contact with Mr Johal’s family and Indian authorities regarding the case.
The Sikh Federation said it has contacted more than 100 MPs who are concerned about the case.
Bhai Amrik Singh, chair of the Sikh Federation, said: “The callous actions of the Indian authorities are sickening, but the Foreign Office and the British High Commission appear to be under pressure not to act and will be accused of looking the other way.
“The Prime Minister and Foreign Secretary will feel our pressure in the next seven days in Parliament via hundreds of MPs who have been contacted by constituents who are unhappy with the lack of action to secure Jagtar’s immediate release and return to the UK.”