Several thousand people marched through Moscow on Wednesday to support detained or jailed anti-Kremlin protesters, a day after President Vladimir Putin accused Washington of supporting a protest movement against him.

Led by anti-corruption blogger Alexei Navalny, the protest dubbed the "March Against Butchers" was aimed at supporting twelve activists accused of violence at an opposition rally last year as well as jailed activists.

"One, two, three, Putin leave!" and "Russia without Putin", chanted the protesters as they marched through central Moscow carrying anti-Putin banners and flags of all hues.

Some wits chanted "Lyudmila without Putin," in reference to Putin's stunning announcement that he was divorcing his wife Lyudmila of 30 years.

Some 7,000 to 10,000 people participated in the march, according to AFP correspondents, while police put the turnout at 5,000 people.

Navalny joined other prominent Russians like Mikhail Kasyanov, the former prime minister turned opposition leader, and poet Dmitry Bykov who rubbed shoulders with liberal and leftist activists amid a heavy police presence.

Anastasia Yuriyeva, a 21-year-old student, said she joined the march to demand freedom for the twelve accused of violence at the rally on the eve of Putin's inauguration for a third term last May.

"They are behind bars without any reason," she said. Ten are in jail, while the 11th is under house arrest and the 12th is under oath not to leave the country.

Yury Kosmynin, a manager, said he wanted Russia to be a democratic country. "Putin should have been fired a long time ago," he said. "His place is in prison."

Some at the march held pictures of Mikhail Khodorkovsky, a former oil tycoon who has been behind bars since 2003 after he fell foul of the Kremlin for his support of the opposition.

Others called on the authorities to free two members of the Pussy Riot punk rock band who are serving two-year sentences for an anti-Putin stunt in a Moscow church.

"Putin is a shame for the country" and "Down with the presidential autocracy" read some of the banners.

The opposition has been struggling to sustain the momentum of the protest movement in the face of a tough crackdown on dissenters unleashed after Putin returned for a third presidential term last May despite huge protests against his 13-year rule.

The march, timed to coincide with the Day of Russia, a national holiday, comes after Putin on Tuesday evening accused Washington of supporting the opposition against him.

"Our diplomatic services do not actively cooperate with Occupy Wall Street, but your diplomatic service actively cooperates and directly supports (Russian opposition)," Putin told Western and Russian staff of the English-language state-funded television channel RT.

"In my view, this is wrong because diplomatic services should be building relations between states and not get involved in domestic affairs."

Putin has earlier accused the State Department of financing the protest movement against him, acidly saying it was "money thrown to the wind."

Two dozen people face jail over their involvement in last year's rally in a criminal probe activists have condemned as a throwback to the Stalin era.

Navalny himself faces up to 10 years in prison on charges of embezzling half a million dollars in a timber deal.

Critics say the trials of the opposition activists are part of an unprecedented clampdown which has also seen a string of tough laws fast-tracked through parliament over the past few months.

On Tuesday, the State Duma lower house passed two controversial bills that impose jail terms for people promoting homosexual "propaganda" to minors and those who offend religious believers.