Nadezhda Tolokonnikova and Maria Alyokhina, in Sydney to speak at a festival, spent 22 months in jail after staging a protest performance in a Moscow cathedral in 2012.
"We think that this person has no place at the G20," Alyokhina told a packed Sydney Opera House audience through an interpreter.
Australian Prime Minister Tony Abbott said this week that calls for Putin to be excluded from the G20 talks in Brisbane in November given the situation in Ukraine were weighing on his mind.
"It's not a decision which Australia really has a right to make unilaterally," he told reporters on Friday.
Abbott has described Russia's involvement in Ukraine as that of a bully and has warned Putin he faces becoming an international outcast unless he keeps his forces within their borders.
"If, as seems to have been the case, Russian armed forces have simply moved across the border, that is an invasion," Abbott said Friday. "And it is utterly reprehensible."
The two Pussy Riot women were convicted over their performance critical of Putin in a Moscow cathedral in 2012. They had almost served their sentences in full when they were freed under a general amnesty in December.
Speaking at the Festival of Dangerous Ideas, the women said the situation in Russia was so repressive they would not now be able to repeat their cathedral performance.
"Unfortunately it wouldn't be even one second of our performance," said Alyokhina, saying a planned performance in Sochi during the Winter Olympics earlier this year was cut short by authorities.
"Now it's impossible to do anything."
The pair again insisted they remained members of Pussy Riot, saying "anybody can be a member", and said they would push ahead with their efforts to defend the rights of prisoners.
Tolokonnikova acknowledged that for some people in Russia, their case had been an impetus for political activity.
"We have a voice and we hope that we use this voice correctly," she said.
