GROZNY — Chechen women said Friday that they had been harassed and some physically harmed by bands of men for not wearing headscarves during the Muslim fasting month of Ramadan.

Bearded men in traditional Islamic dress have been roaming the streets both on foot and in cars since Ramadan started on Aug. 11, demanding bareheaded women wear a headscarf, Grozny residents and witnesses said.

"Two men came up to me, one furiously fingering a prayer bead, and said it wasn't pretty to have a bare head during Ramadan," said Markha Atabayeva, 38. "They instilled such fear in me."

Atabayeva said she had seen a group of men with automatic rifles taunting women for not wearing headscarves.

Atabayeva was one of at least a dozen women who told of harassment or attacks. A woman in her mid-30s said she was punched in the face by a man in Islamic dress after refusing to put on a headscarf he had given her.

One of the women's assailants said in an interview that "hundreds" of women had been warned.

"We are trying to warn women of their possible sins before God," the assailant, who described himself as an "activist," said on condition on anonymity. "We do this through force, fighting and battles."

Another assailant said they were working under orders from Chechnya's Center for Spiritual-Moral Education, which Chechen President Ramzan Kadyrov set up 18 months ago.

Kadyrov's spokesman declined to comment on the action against women failing to wear headscarves. Alcohol is all but banned in Chechnya, and women must wear headscarves in state buildings. Polygamy is encouraged by authorities.

The men's action follows an order earlier in the week from Chechnya's spiritual leader to shut all cafes during Ramadan, as well as paintball attacks on bareheaded women in June.

A number of other women last week described how men in cars threatened them with violence if they did not cover up. While some women carry headscarves in their bags, those without were encouraged to go home immediately.