LONDON — The anonymous letters arrived this weekend in plain white envelopes with second-class stamps, and were sent to people in at least six communities in England.

Inside was a message so hateful that it sent out ripples of alarm and prompted a national counterterrorism investigation.

The message said that April 3 would be “Punish a Muslim Day,” and that points would be awarded for acts of violence: 25 points for pulling off a woman’s head scarf, 500 points for murdering a Muslim and 1,000 for bombing a mosque.

Riaz Ahmed, a Liberal Democrat councilor in Bradford, in West Yorkshire County, said he had received one of the letters at his business address.