The Russian lower house of parliament on Tuesday approved in a first reading a Kremlin-sponsored bill on amnesty that could see the jailed members of the Pussy Riot band released early.

But under the proposed measure there would be no clemency for the former oil tycoon Mikhail Khodorkovsky and many of the opposition demonstrators accused of using violence against police at a protest a day before President Vladimir Putin's inauguration last year.

The amnesty will not include people "who committed crimes highly dangerous to the public, crimes that used violence or the threat of violence" and those who committed crimes or regular violations while serving their sentence, according to the text of the amnesty bill.

The amnesty does not have to be approved by the upper house of parliament and could go into effect one day after the scheduled second and third readings in the Duma on Wednesday.

The bill has been heavily criticised by rights activists as a largely cosmetic measure that does not go far enough.

The jailed members of Pussy Riot punk band, Nadezhda Tolokonnikova and Maria Alyokhina, who are serving two-year sentences on charges of hooliganism for staging an anti-Putin protest in a cathedral, could be released by the end of the week, Tolokonnikova's husband said.

"Prison officials say they will free them right away - on Thursday," Pyotr Verzilov wrote on his Twitter blog.

The two young mothers, who have been in jail since March 2012, had been set for release in March.

There has also been hope that the amnesty will apply to 30 foreign and Russian Greenpeace activists who are awaiting trial on hooliganism charges after their open-sea protest against Arctic oil drilling in September.

Rights activists have also hoped that the amnesty will free protesters arrested under the so-called Bolotnaya probe after a mass protest against Putin on Bolotnaya square in Moscow on May 6, 2012, twelve of whom are currently on trial.

However Putin said that those accused of hitting policemen do not deserve to be freed early, and only the few protesters accused of merely participating in the 2012 rally are likely to walk out of prison.

As it stands, the bill would require a conviction for the amnesty to apply.

However Kommersant newspaper said on Tuesday, citing Kremlin sources, that the measure is likely to be extended to include those on trial or under investigation as well.