(CNN) -- Russian lawmakers backed a sweeping amnesty law Wednesday that could see jailed members of the Pussy Riot punk protest band released early and arrested Greenpeace activists avoiding prison, the state-run RIA Novosti news agency reported.
The law received enough votes in favor in the Duma that it does not require President Vladimir Putin's signature, Ria Novosti said.
The amnesty, to mark the anniversary of the adoption of Russia's post-Communist constitution in 1993, will be applied to thousands of Russian prisoners, the agency reported.
It is due to take effect on Thursday, according to the Russian government daily newspaper, Rossiyskaya Gazeta.
Pussy Riot's Nadezhda Tolokonnikova and Maria Alyokhina are serving two-year jail terms for their part in a performance critical of Putin, when he was Prime Minister.
The performance was held at a Russian Orthodox cathedral in 2012, and the musicians were found guilty of hooliganism.
The women, set to complete their sentences in coming months, have young children and would therefore qualify for the amnesty, RIA Novosti said.
In September, 30 people were arrested after a Greenpeace protest at an offshore oil platform in the Arctic and charged with hooliganism. They were told they would face trial.
"With the amnesty also extended to individuals on trial, however, the group may be free from prosecution and its foreign members be allowed to return home," RIA Novosti said.
Russia's record on human rights is in the spotlight as the country prepares to host the 2014 Winter Olympics in Sochi in February.
CNN's Olga Pavlova in Moscow and Marie-Louise Gumuchian in London contributed to this report