As many as 300 anti-Putin protesters took over a Moscow square for most of the day Tuesday until hundreds of helmeted riot police swept in to disperse the young crowd, detaining some of them seemingly at random.

The impromptu rally had moved to the Chistiye Prudy square after police broke up a demonstration by hundreds of opposition activists who had spent the night outside the presidential administration offices to protest Vladimir Putin's return as Russia's president.

Two prominent opposition leaders were detained by police in the early hours of Tuesday but later released. They then joined up with dozens of their supporters who had moved on to Chistiye Prudy, or Clean Ponds, where they vowed to continue the roving protest.

"If we are pushed away from here, we'll move to other squares," said Sergei Udaltsov, the leader of a leftist movement. "The objective is to have people on the squares every day who are struggling for freedom, for change. It is a very simple tactic, and I think it has a chance to bring a successful result."

The cat-and-mouse game between protesters and police began on Monday, the day of Putin's inauguration at a formal ceremony inside the Kremlin. Hundreds of activists tried to protest near Red Square and along the route Putin's motorcade took to the Kremlin, but they were turned back or detained by thousands of riot police.

Police said they made about 300 detentions on Monday, but in some cases the same people were detained and then released more than once.

On Tuesday, police reported at least 30 detentions.

At Chistiye Prudy, the protesters gathered peacefully without any posters or flags, braving a heavy rain and singing along as a young man strummed a guitar. As soon as the approaching riot police were spotted, the protesters cleared out and headed for a third square.

In Washington, U.S. State Department spokesman Mark Toner said "we are disturbed by images of police mistreatment of peaceful protesters, both during the protests and after detentions."

The U.S. and Russia had made significant process in their relationship, he said, but "we're going to continue to raise human rights issues when we have concerns, and this is one of those cases."

Tens of thousands attended anti-Putin protest rallies in the months before the March election. Since then the numbers have dwindled, but the protest movement has shown an unexpected resilience. A demonstration on the eve of the inauguration drew well more than 20,000.

Putin has been in power since 2000, first as president and then for the past four years as prime minister. He has just begun a six-year term and would be eligible for a fourth term.