TWO members of Russian punk protest band Pussy Riot have been freed from prison, deriding President Vladimir Putin's amnesty that led to their early release as a propaganda stunt and promising to fight for human rights.

Nadezhda Tolokonnikova, 24, shouted "Russia without Putin" following her release from a Siberian prison, hours after band mate Maria Alyokhina, 25, was freed from jail in Nizhny Novgorod.

They walked free days after former oil tycoon Mikhail Khodorkovsky was released under a pardon from Mr Putin after more than 10 years in jail, a move widely seen as intended to improve Russia's image before it hosts the Winter Olympics in February.

Tolokonnikova told reporters outside prison in Krasnoyarsk: "The border between being free and not free is very thin in Russia, a totalitarian state."

She and Alyokhina were sentenced to two years in prison for a profanity-laced protest against Mr Putin in a Russian Orthodox church in 2012 after a trial Kremlin critics said was part of a clampdown on dissent in his third presidential term.

The case caused an outcry in the West but there was much less sympathy for the women at home than abroad.

They had been due for release in early March. Mr Putin, who denies jailing people for political reasons, has said the amnesty would show that the Russian state is humane.

However, the measure will not benefit opposition leader Alexei Navalny, a vocal Putin foe who will be kept out of elections for years by a conviction and five-year suspended sentence on a theft charge he says was Kremlin revenge for his activism.

After her release, Alyokhina said the amnesty was far too narrow and aimed at deflecting criticism over human rights before the Olympics in Sochi in February.

She said: "I do not think it is a humanitarian act, I think it is a PR stunt. My attitude to the president has not changed."

Tolokonnikova, who staged a hunger strike earlier this year and drew attention to stark conditions and long hours of mandatory labour in the jail where she was previously held, said she would fight for prisoners' rights.

"Everything is just starting, so fasten your seat belts," she said, suggesting Pussy Riot - jailed for a "punk prayer" in the main cathedral of Russia's dominant faith - would continue to use attention-grabbing protests to make their point.

"I think we will unite our efforts in our human rights activity ... the methods which we will use will remain the same," Alyokhina said in Nizhny Novgorod. "We will try to sing our the song to the end."

Alyokhina said she would have rejected the amnesty if that been a option. She said she wants to focus on human rights including the rights of prisoners.

"I'm not afraid of anything any more - believe me," she said.

In addition to the amnesty, Putin unexpectedly pardoned Khodorkovsky, the former Yukos oil company chief who had been in jail since his arrest in 2003 and conviction in two trials that Kremlin critics said were punishment for challenging Mr Putin.

Khodorkovsky, who was freed on Friday and flown to Germany, said Mr Putin is seeking to improve his image while also showing that he is confident in his grip on power after weathering large opposition protests and winning a third term last year.

Mr Putin wants to send "a signal to society and the world that he feels secure and is not afraid", Mr Khodorkovsky said.

The amnesty is also expected to enable 30 people arrested after a Greenpeace protest against Arctic oil drilling to avoid trial on hooliganism charges, removing another irritant in ties with the West. They faced up to seven years in prison jail if convicted.

Mr Putin said the amnesty was not drafted with the Greenpeace activists or Pussy Riot in mind. Rights activists have estimated the amnesty will free fewer than 1500 of the 564,000 convicts in Russian prisons.

A third Pussy Riot member, Yekaterina Samutsevich, was freed last year when a judge suspended her sentence on appeal.