* Chechen women say targeted for not wearing headscarves

* Raids follow Ramadan cafe ban, paintball attacks

(Repeats with no editorial changes)

GROZNY, Russia, Aug 20 (Reuters) - Many women in Russia's volatile Chechnya region said on Friday they had been harassed and some physically harmed by bands of men for not wearing headscarves during the Muslim fasting month of Ramadan.

Against the backdrop of a spreading Islamist insurgency, many fear that growing interest in radical Islam could fuel separatism in the volatile North Caucasus, where the Kremlin watches uneasily as sharia law eclipses Russian.

Residents and witnesses told Reuters that bearded men in traditional Islamic dress have been roaming the streets both on foot and in cars since Ramadan started on Aug. 11, demanding bare-headed women wear a headscarf.

"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," 38-year old Markha Atabayeva told Reuters in the Chechen capital Grozny. "They instilled such fear in me".

Atabayeva was one of at least a dozen women who told of harassment or attacks. One of the women's assailants told Reuters "hundreds" of women had been warned.

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

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.

The men's action follows a radical order earlier this week from Chechnya's spiritual leader to shut all cafes during the month of Ramadan [ID:nLDE67H17B], as well as paintball attacks on bareheaded women in June.

ISLAMIC RULES

A number of other women described this week 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.

The action targeting women highlights tension over efforts by Chechnya's firebrand Moscow-backed leader, Ramzan Kadyrov, to enforce Islamic rules that can violate Russia's constitution.

One of the assailants, who described himself as an "activist", told Reuters: "We are trying to warn women of their possible sins before God".

"We do this through force, fighting and battles," he said on condition of anonymity, adding that hundreds of Chechen women had been "warned" since the start of Ramadan.

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

Critics say that in return for keeping a shaky peace in Chechnya, site of two separatist wars with Moscow since the mid-1990s, Kadyrov is allowed to impose his vision of Islam.

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.

Analysts say the gradual encroachment of Islamic sharia law in the mainly Muslim North Caucasus, where rebels are fighting to create a pan-Caucasus state governed by sharia law, deals a major blow to Kremlin efforts to control the region. (Writing and additional reporting by Amie Ferris-Rotman; Editing by Charles Dick)