The two members of the Russian activist collective Pussy Riot who remain imprisoned were both denied parole this week. On Friday, Nadezhda Tolokonnikova was told by a court in Saransk that she had not sufficiently repented for her act of “hooliganism” in performing at a Moscow Orthodox cathedral last year. Maria Alyokhina received similar news from a court in Perm on Wednesday. Both are being held in prisons near their courts, and are not expected to be released until next year.

Ms. Tolokonnikova appeared in court to testify but Ms. Alyokhina, who recently undertook what she said was a successful hunger strike to protest conditions in prison, was permitted to speak only via video link. Supporters of the group, who received international notoriety for a 40-second anti-Kremlin “punk prayer” in the cathedral, had hoped that their sentences would be commuted; a third imprisoned member, Yekaterina Samutsevich, was released in October.

Last week Amnesty International issued an open letter calling for the women’s release; it was signed by more than 100 musicians and artists, including Bruce Springsteen, Madonna, Paul McCartney, Radiohead, Arcade Fire, Harry Styles and Adele.

Artistically, the collective, known for pop-up appearances in bright dresses and balaclavas, has been relatively silent as the Russian government has drafted laws seemingly aimed at them, from banning the wearing of masks in public to a blasphemy bill that stiffens the penalty for insulting religion. A video released last week that appeared to be by Pussy Riot – promoted via YouTube and Twitter accounts associated with the group – was in fact by imitators, according to a message posted later on FreePussyRiot.org.

“As we struggle against the system in the courts and prisons, and thus do not have the opportunity to perform new actions, a group of anonymous activists presented a gift to us — by releasing a music video,” the message said. It went on to support the sentiments in the video – which criticized President Vladimir V. Putin, his allies and the misappropriation of oil wealth – while also distancing Pussy Riot from lesser imitators.

“Those who want to help us, may not take possession of our ideas in order to pervert them from inside and then chase us out of the group using our openness and anonymity as an argument,” the message read. “If the new group is able to copy all that what we have created in a better way, we will welcome them joyfully.”

The message hints at the complications of running an anonymous, radical art collective: the music video was promoted through an account run by Pyotr Verzilov, the husband of Ms. Tolokonnikova; she was also said to contribute lyrics to the song. But a post by Ms. Samutsevich on Twitter suggested it was not an official Pussy Riot work. Mr. Verzilov and Ms. Tolokonnikova were also part of another notorious Russian art group, Voina, and exhibited a video in the Moscow Biennial under that group’s name in 2011, but the group protested, saying they had been removed as Voina members in 2009.

“Kill Voina! Free Pussy Riot!” an unincarcerated member of Pussy Riot, who goes by the pseudonym Fara, wrote on Twitter last week.

But whatever their differences, the members remain united in supporting their jailed comrades. “Nadia, hold on,” another pseudonymous member, Shaiba, wrote after Ms. Tolokonnikova’s parole was denied. “We will show them! ¡No pasarán!”