A Russian court has rejected parole for jailed Pussy Riot band member Maria Alekhina, despite a high-profile plea from former Beatle Paul McCartney and other top musicians.

Earlier this week, supporters of the provocative feminist punk rockers revealed a recent letter written by McCartney in which the famed musician calls for the release of and parole for both Alekhina and bandmate Nadezhda Tolokonnikova.

Peter Gabriel and Patti Smith also penned letters supporting the two jailed Pussy Riot members.

The pair are currently serving two-year sentences after being convicted of "hooliganism motivated by religious hatred" for their now infamous and irreverent punk protest against Vladimir Putin at Moscow's main cathedral in March 2012.

A third convicted Pussy Riot member, Yekaterina Samutsevich, had her sentence suspended on appeal last fall.

Making his request "in a spirit of friendship for my many Russian acquaintances who, like me, believe in treating people — all people, with compassion and kindness," McCartney addressed his letter to the Russian court hearing the parole appeal. Alekhina began a hunger strike on Wednesday after she was barred from attending her own parole hearing.

In denying Alekhina's appeal on Thursday, the court accepted a claim by prosecutors that she had systematically disobeyed prison authorities and failed to repent for her crime, according to reports by Russian media. Her lawyer vowed to appeal Thursday's decision.

In late April, the same judge rejected Tolokonnikova's request for early release on parole.

Fans around the globe have continued to support the jailed activist musicians, who protested against Russia's increasing authoritarianism under Putin. Protests and music festivals have been held in their honour, while famous names, including Pete Townshend, Jarvis Cocker and Madonna, have called for their release.

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Early parole requests for jailed Pussy Riot members Maria Alekhina, left, and Nadezhda Tolokonnikova have been denied. (Natalia Kolesnikova/AFP/Getty Images )