At least 20,000 Russians marched through Moscow on Sunday to protest a Kremlin law banning US adoptions of Russian orphans in a move the opposition hopes will breathe some life into the faltering protest movement.

The protest, dubbed the "March Against Scoundrels," was aimed at naming and shaming lawmakers who fast-tracked the anti-adoption bill through the lower house of parliament, the State Duma.

Participants carried pictures of President Vladimir Putin and lawmakers such as Alina Kabayeva, a former gymnast, and Irina Rodnina, Russia's Olympic gold medal figure skating champion, who voted for the measure.

Protesters stamped the word "Shame!" across their portraits in red, and a poster of Putin had mud thrown at it.

The Duma passed the bill without debate in a quick 420-7 vote during a third and final reading in December.

The latest anti-Kremlin march came after Putin signed off on a measure introducing a blanket ban on US adoptions in reprisal for Washington legislation targeting alleged Russian rights abusers.

"I am against our Duma and the thieving authorities," Yulia Shamanova, a young mother, told AFP.

"This is a very shameful law that should be cancelled."

One placard at the march read "Stop lying," while another said in English: "American parents, thank you for healing our orphans."

The marchers were also heard chanting "Shame," and "the Duma is eating children."

Moscow authorities had said no more than 20,000 people could participate in the protest and at least that number took part in the march amid a heavy police presence and temperatures of minus 12 degrees Celsius (seven degrees Fahrenheit), an AFP photographer said.

Leftist activist Sergei Udaltsov said up to 50,000 had turned up, while city police put the turnout at just under 10,000.

"A little goes a long way," said march participant Alexei Sharapanyuk.

"Sooner or later something will change in the country. It is no longer possible to tolerate this."

Political activists have taken up the cause of Russian orphans to also make a broader point about widespread rights violations and called for the Duma's dissolution.

They have hoped public anger may help revitalise the protest movement, which lost momentum in a tough crackdown on civil society that followed Putin's Kremlin comeback in May.

Only a few thousand attended an unsanctioned rally in December, a tiny fraction of the 120,000 people who came out at the height of the protests one year ago.

"I am marching against scoundrels," tweeted Alexei Navalny, the anti-Kremlin movement's most charismatic leader.

Putin's spokesman said the president was aware of the protest.

Speaking to Dozhd, a private television channel, Dmitry Peskov praised march participants for drawing attention to the plight of orphans but added that calls for the Duma's dissolution were "unconstructive."

At the end of the march, which lasted around 2.5 hours, some participants threw the portraits of lawmakers and Putin into a garbage bin, while others burnt them, Udaltsov said on Ekho of Moscow radio.

Critics say the ban has robbed many disabled orphans of the chance to receive adequate medical treatment abroad, dealt a blow to US-Russian relations and triggered a rare split in the government.

More than 100,000 signatures have already been collected against the anti-adoption measure and the Novaya Gazeta opposition newspaper has also collected more than 117,000 signatures on a petition calling for the dissolution of parliament.

Observers say the latest Kremlin initiative has led to a huge split in society and dented the government's moral authority.

Andrei Isayev, chairman of the Duma committee responsible for labour, social policies and veterans' affairs, had earlier branded those planning to take to the streets "enemies" of Russia.

Smaller rallies took place in other cities.

Around 1,500 gathered in Saint Petersburg, Putin's hometown, with some holding placards reading "Putin is evil."