The freed members of the Pussy Riot punk band said Friday they still wanted Russian President Vladimir Putin out of power and would like freed ex-tycoon Mikhail Khodorkovsky to replace him.

Nadezhda Tolokonnikova, 24, and Maria Alyokhina, 25, made their call for the Russian strongman to go at their first news conference, hosted by an opposition television channel and clearly aimed at touting them as figures of national importance.

"As far as Vladimir Putin is concerned, our attitude towards him has not changed," Tolokonnikova said alongside Alyokhina on the premises of opposition television station Dozhd.

"We would still like to do what they put us in jail for. We would still like to drive him out," said the brunette.

In February 2012, several members of Pussy Riot jumped around the altar of the church and attempted to sing what they called a "punk prayer" calling on the Virgin Mary to "drive Putin out."

Tolokonnikova, said she would like Kremlin critic Mikhail Khodorkovsky, who was last week released under a pardon, to run for president.

"I would very much like to invite Mikhail Borisovich to this post," referring to the Kremlin critic, who spent more than a decade in jail, by his first name and patronymic.

"I am in solidarity with that," added the curly-haired Alyokhina.

Asked to describe Putin, Tolokonnikova said he was "closed, non-transparent" and "a chekist," using a Soviet-era term for a member of security services.

Alyokhina slammed the top-down political system the former KGB agent has built over his decade in power.

"There are constant conspiracies, constant suspicions," she said. "If a person is trying to control everything, has made this his main goal, then sooner or later -- and most likely sooner -- control will slip out of his hands."

Speaking to a forest of microphones during their first news conference since their release from prison earlier this week, the young women fielded a deluge of questions from Russia and abroad.

In a possible nod to Putin's televised call-in marathons, the two-hour news conference was dubbed "a direct line with Pussy Riot."

Famous Soviet-era dissident Vladimir Bukovsky, who the rocker-activists described as their role model, called in from Cambridge in England to wish them success in their future endeavours.

'System should be on its toes'

The band members said they would now focus their energy on establishing a rights group to protect prisoners in Russia's notorious jails.

Tolokonnikova said they would accept donations to set up the rights group and would work with prominent opposition leader Alexei Navalny.

Khodorkovsky, who walked out to freedom last Friday, also stressed he would like to work toward releasing Russia's "political prisoners," and Tolokonnikova invited him to join forces.

The women said that now that they had seen the prison system from the inside they would like to help change it.

"The system should be on its toes. We will make it be on its toes," she said.

The Pussy Riot members have also called for the boycott of the Winter Olympic Games Russia hosts in Sochi in February.

Alyokhina said on Friday that a decision to visit the games was a "political choice" and everyone who was going should remember about Russia's prisoners.

Earlier Friday the young women, who both have small children, arrived back in Moscow after reuniting in Siberia.

Their release two months early from their two-year prison terms came after an amnesty backed by Putin. The amnesty has also seen the end of the prosecution of the Arctic 30 Greenpeace activists held by Russia over a protest.

After the stunt at the Christ the Saviour Cathedral three of the five rockers -- Alyokhina, Tolokonnikova and Yekaterina Samutsevich, 31 -- were identified, later arrested and in August 2012 found guilty on charges of hooliganism motivated by religious hatred.

Samutsevich was released in October after being given a suspended sentence, but a Moscow city court upheld on appeal the two-year prison camp terms for Tolokonnikova and Alyokhina.

On Friday, Tolokonnikova defended her stunt in 2008 which saw her, her husband and several members of Voina (War) performance art group engage in group sex in a museum to mock Putin's protege Dmitry Medvedev who was set to take over the presidency from his mentor in stage-managed elections.

"The whole country was put in the doggy position," Tolokonnikova said Friday, acknowledging however she would not perform such a stunt these days.