At least 20,000 Russians have marched through Moscow this afternoon to protest against a Kremlin law banning US adoptions of Russian orphans.

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

The march comes after President Vladamir Putin signed off on a measure introducing a blanket ban on US adoptions, in reprisal for Washington legislation targeting alleged Russian rights abusers.

More than 100,000 signatures have already been collected against the anti-adoption measure.