MOSCOW - Russian opposition parties walked out of parliament on Wednesday in a rare act of protest against disputed regional elections, with the Communist Party blaming Vladimir Putin for an unworkable system of governance.

Walkout leaders demanded a meeting with President Dmitry Medvedev and a recount of votes after independent observers said nationwide mayoral, regional and district elections on Sunday were rigged and turnout was much lower than reported.

In the vote, the United Russia party -- backed by Medvedev and nominally led by Prime Minister Putin -- retained power in key locations, including Moscow, the most populous and affluent region.

Medvedev would not talk to the opposition face to face for at least 10 days as it is not on his schedule, his spokeswoman Natalya Timakova told reporters in Moscow on Wednesday.

Medvedev has pledged to increase openness in society and tackle corruption, and has hailed the vote.

None of the three protesting parties, the Nationalist Liberal Democratic Party (LDPR), Fair Russia and the Communist Party, are usually critical of the Kremlin.

Liberal opposition parties are not represented in the Duma, or parliament, and are marginalized in state media.

Putin, speaking to reporters in Beijing late on Wednesday, said he was pleased with the election results.

Those who don't win are never happy, he said, adding that any issues should be fought over in court.

Vadim Solovyov, a Communist Party deputy at the Duma, told Reuters by telephone: What's the point in having a legal system and laws if they only suit one party?... Putin's system of government makes no sense and it simply doesn't work.

LDPR leader Vladimir Zhirinovsky, who led the walkout, demanded a meeting with the president. He later told a news briefing inside the parliament: The elections were rigged. This is outright fascism... We demand a recount of all votes.

Communist leader Gennady Zyuganov echoed him. Our president happily fights corruption but ignores the entire sphere of opposition here, he said to roaring applause from around 20 grey-haired members from his party.

Wearing his characteristic red tie and hammer and sickle pin, Zyuganov said his party would present a list of demands to Medvedev, including open political dialogue and allowing the opposition to advise on the financial crisis.

The party in power is obliged to get us out of this crisis... But we have our own methods too.

The Communists said they were also considering a Supreme Court appeal.

NEW LOW FOR RUSSIAN POLITICS

Solovyov said Russia's political situation had plummeted to a new low. At least during the (President Boris) Yeltsin era we kept some Soviet systems that worked. But with Putin, it's pointless and Russia's the worst it has been.

Interfax quoted United Russia Chairman Boris Gryzlov as saying, I am outraged by today's events. The opposition's sabotage of the plenary session will not disrupt it.

He added that populist campaigns are pointless.

Medvedev, welcoming the elections' results on Monday, said it was the ruling party's moral, but also legal right to run the regions.

Zhirinovsky had said his party would not participate in parliament until Medvedev meets them.

United Russia holds more than two-thirds of the seats in the Duma and can still vote in new legislation.

Russia's Central Election Commission chief Vladimir Churov, commenting on the surprise walkout, told Interfax, No comment. It is just politics. Churov has already derided complaints about the elections as improper hysteria.

(Additional reporting by Daria Korsunskaya in Beijing and Oleg Shchedrov in Moscow)

(Editing by Sonya Hepinstall)

Dmitry Medvedev Putin Vladimir putin