Police officials have identified the killer as Shambhu Lal Raigar, an on-again, off-again marble trader in his mid-30s. He was arrested on Thursday morning hiding at a relative’s house. According to police officials, Mr. Raigar confessed to the crime. He says as much on video, appearing in front of a statue of a Hindu god. “It may be good or bad, but I’ve done it,” he says. “If I have to die, then why not kill and die?”

The victim, seen in the video as a blurry image wearing a white Muslim prayer cap, was identified as Afrajul, a 50-year-old migrant laborer from the eastern state of West Bengal. Activists in the area said they did not know how much truth there was to the accusation that Mr. Afrajul, who was married with three children, was having an affair with a Hindu woman.

There is no doubt, however, that the subject of relations between Muslim men and Hindu women is a flash point.

Across India, Hindu supremacists have accused Muslim men of carrying out what they call “love jihad.” Hindu activists have urged young Hindu women to be on the lookout for Muslim men trying to lure them into marriage in order to convert them. Some politicians have turned “love jihad” into a rallying cry, using it to win votes — and polarize communities.

India’s Supreme Court is currently trying to untangle a messy case of a Hindu family in Kerala that said their daughter was forced to convert to Islam after being recruited by Islamist extremists. The young woman sharply disagreed, saying that she had converted voluntarily and that she wanted to live with her husband.

Little is known about Mr. Raigar, the killer in the video, who comes across on camera as educated and calculated. He speaks at length about how black-clad jihadists want to destroy his community. He refers to the mosque demolition that happened in 1992.

He first posted his videos on a WhatsApp group, Rajasthan activists said, and people in his community began forwarding it. According to the activists, Mr. Raigar lured Mr. Afrajul to a thinly populated area outside of Rajsamand, a midsize city, by promising him work as a day laborer.

At the end of the killing video, Mr. Raigar sprinkles kerosene on Mr. Afrajul’s body, sets it on fire and calmly walks away.