The European Union has demanded the release of detainees from Russia
The US state department said protesters should be able to "exercise their rights without fear of retribution".
The protesters urged PM Dmitry Medvedev to quit over corruption allegations. Russia's main opposition leader, Alexei Navalny, who called the protests and was one of those arrested, appeared at court on Monday. Mr 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 Mr Medvedev should be summoned by the court as the chief organiser of the protests. Mr Navalny has yet to go before a judge but is likely to face charges relating to organising banned protests and could be held for 15 days.
Sunday's 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 organised without official permission. TV pictures 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." US 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."