The EU has demanded the release “without delay” of more than 500 people detained in protests across Russia on March 26.
The US state department also said protesters should be able to “exercise their rights without fear of retribution”.
The protesters urged Russian Prime Minister Dmitry Medvedev to quit over corruption allegations.
Russian opposition leader Alexei Navalny, who called the protests and was one of those arrested, appeared at court on March 27.
Alexei Navalny, 40, tweeted from the building: “Hello everyone from Tversky Court. The time will come when we will have them on trial (but honestly).”
He also said that PM Dmitry Medvedev should be summoned by the court as the chief organizer of the protests.
March 26 protests drew thousands of protesters nationwide, including in Saint Petersburg, Vladivostok, Novosibirsk, Tomsk and several other cities, as well as Moscow.
At least 500 protesters were detained. Most of the marches were organized without official permission.
TV footages showed demonstrators chanting “Down with [Russian President Vladimir] Putin!”, “Russia without Putin!” and “Putin is a thief!”.
Correspondents say the marches appear to be the biggest since anti-government demonstrations in 2011 and 2012.
An EU spokesman said the Russian police action had “prevented the exercise of basic freedoms of expression, association and peaceful assembly, which are fundamental rights enshrined in the Russian constitution”.
The statement added: “We call on the Russian authorities to abide fully by the international commitments it has made… and to release without delay the peaceful demonstrators that have been detained.”
State Department spokesman Mark Toner said in a statement: “The Russian people, like people everywhere, deserve a government that supports an open marketplace of ideas, transparent and accountable governance, equal treatment under the law, and the ability to exercise their rights without fear of retribution.”
Alexei Navalny called for the nationwide protests after he published reports claiming that PM Dmitry Medvedev controlled mansions, yachts and vineyards – a fortune that suggests income that far outstrips his official salary.
His report, posted on YouTube, has been viewed more than 11 million times.
It includes the accusation that Dmitry Medvedev had a special house for a duck on one of his properties – and on March 26, some demonstrators held up images of yellow rubber ducks.
Others showed up with their faces painted green, a reference to a recent attack in which Alexei Navalny was hit with green liquid.