A Russian court refused on Thursday to free three members of a women's punk band that sang a protest song against Vladimir Putin in a cathedral, despite calls for their release by activists and backers who scuffled with police at the hearing.

The three have been in detention for weeks over Pussy Riot's performance in short dresses and bright masks which offended Russian Orthodox believers but also ignited a debate on Church-state relations.

Amnesty International has called for the women's release and lawyers for the three asked the Moscow court to free them on bail on Thursday.

But the court extended their detention until June 24 after prosecutors said investigations were still continuing into the protest in which five group members burst into Moscow's Christ the Saviour Cathedral on February 21 and sang at the altar.

The judge set no date for a trial in separate, back-to-back hearings that reviewed their pre-trial detention. Each faces up to seven years in jail if found guilty of hooliganism over the rendition of Holy Mother, throw Putin out!

Amnesty said earlier this month the three were members of Pussy Riot but all denied taking part in the masked protest.

This is a political case. It is clear that Russia has now decided to crack down on all opposition activists, Yekaterina Samutsevich told journalists in the packed courtroom.

Her colleague Maria Alyokhina also said their cases were politically motivated and complained she had not been allowed any contact with her family while in detention.

Referring to the pre-determined show trials of the late 1930s under Soviet leader Josef Stalin, she said: If for criticising the authorities I can't even hear the voice of my own child, welcome to 1937.

The third band member, Nadezhda Tolokonnikova, also made an ironic reference to the Communist era, telling reporters she was spending her time in jail reading First Circle, a novel by Alexander Solzhenitsyn about the Soviet labour camp system.

Lawyers for the three said they would appeal to the European Court of Human Rights.

But state investigators said the three should be kept in detention to prevent them fleeing Russia, being attacked by their opponents or committing any new offences.

Before the hearings, about 60 people gathered outside the beige brick courthouse chanting Freedom! Freedom!. Some released green, yellow and pink balloons with the group's trademark masks drawn on them.

Two protesters set off flares and scuffles broke out when an Orthodox bystander threw an egg at the husband of one of the band members. Reuters reporters saw police haul away at least 13 protesters and some Russian media put the number of detentions as high as 30.

CHURCH UNDER FIRE

Pussy Riot's action was part of a protest movement against Prime Minister Putin that has lost momentum since he won a presidential election on March 4. The protest was also seen as a challenge to the Church over its involvement in politics.

For me it was an insult. Not only did they climb up to the altar but they turned their backsides to it, said Alexei, a young man outside the court who declined to give his last name.

Kirill says the performance, posted on the Internet, was part of an attack on the Church and has summoned followers to nationwide prayer on Sunday in defence of the faith, desecrated sanctuaries, the Church and its good name.

But anger over the arrests has also triggered criticism of the Church, especially after Kirill called for tough punishment and an aide described Pussy Riot's protest as a crime worse than murder.

There is no dogma against criticising the patriarch. We are meant to respect the patriarch's words, but we do not have to agree with him, said Irina Karatsova, an Orthodox believer who said she had come to the court to support Pussy Riot.

The status of the Church, which was not immediately available for comment, has improved vastly since the Soviet Union collapsed in 1991. More than 70 percent of Russians say they are Orthodox although far fewer are practicing.

The Church is widely accused of being too close to Putin, whose 12-year rule as president and then prime minister was described by Kirill as a miracle of God.

Putin appeared alongside Kirill at an Easter service on Sunday and the Church regularly advises the government on social issues.

(Reporting by Alissa de Carbonnel, Writing by Timothy Heritage, Editing by Steve Gutterman and Andrew Heavens)