Women in Russia's volatile Muslim Chechnya region have said that police had targeted them with paintball pellets for not wearing headscarves.

The attacks highlight tension over efforts by Chechnya's firebrand Moscow-backed leader, Ramzan Kadyrov, to enforce Muslim-inspired rules that in some cases violate Russia's constitution.

A car carrying men in military uniform slowed down to approach us, one started filming on his mobile phone, and when they sped away we noticed paint all over our clothes, a woman in the Chechen capital Grozny said on condition of anonymity.

Several witnesses told Reuters that men in camouflage, which is worn by many Chechen police and security officers, had fired paintball guns at women from cars with tinted windows in multiple incidents this month.

This week, fliers from the self-proclaimed paintballers appeared in the city of Gudermes, site of Kadyrov's opulent residence, warning women that if they did not cover their heads the attackers will be forced to resort to tougher measures.

The Kremlin-backed head of Russia's Muslim Chechnya region has praised assailants who targeted women with paintball pellets for going bareheaded.

Eyewitnesses have said men in camouflage, often worn by police and security forces in the volatile region, fired paintball guns from cars about a dozen times last month at women who were not wearing headscarves.

I don't know (who they are), but when I find them I shall announce my gratitude, Ramzan Kadyrov said in a weekend interview on state-run regional television channel Grozny, according to a Reuters.

The attacks highlighted tension over Kadyrov's efforts to enforce Muslim-inspired rules that in some cases violate Russia's constitution.

Russian rights group Memorial, which has blamed the attacks on law enforcement officers, said in a statement on Thursday: Kadyrov's interview clearly demonstrates the restriction on women's rights in Chechnya -- he openly defends unlawful acts.

Kadyrov called the victims of the paintball attacks naked women who had most likely been forewarned. Even if they were carried out with my permission, I wouldn't be ashamed of it, he said of the paint-pellet attacks.

In the same interview, Kadyrov lambasted journalists and called rights activists enemies of the people.

Chechen women said 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. They instilled such fear in me.

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