Russia's main opposition leader, Alexei Navalny, who called the protests and was one of those arrested, appeared at court on Monday.
The nationwide protest came after Navalny's accusations of government corruption, with smaller demonstrations in St. Petersburg, Vladivostok, Novosibirsk and other cities across Russian Federation.
TV pictures showed demonstrators chanting "Down with [Russian President Vladimir] Putin!", "Russia without Putin!" and "Putin is a thief!".
More than a thousand people were detained on Sunday in Moscow and hundreds more in other cities across Russian Federation after most municipal authorities refused to grant permission for the protests. The Tverskoy District Court in Moscow on Monday fined Mr. Navalny 20,000 rubles ($352) for organizing.
Navalny, a lawyer and anti-corruption blogger who heads Russia's Progress Party, called for the nationwide protests after he published reports claiming that Medvedev controlled mansions, yachts and vineyards - a fortune that far outstripped his official salary.
The bloc called on Moscow to "release without delay the peaceful demonstrators" detained at dozens of rallies across Russian Federation on Sunday.
He said the Kremlin had no problem with people expressing their opinions at protest meetings, but said the timing and location of such events had to be agreed with the authorities in advance, something which he said had not been done in large part on Sunday.
"Essentially what we saw yesterday in several places - probably especially in Moscow - is a provocation and a lie", said Kremlin spokesman Dmitry Peskov on Monday.
Reports earlier on Sunday questioned the Trump administration's silence on the protests, including the White House and State Department.
Meanwhile, the US State Department "strongly condemned" the detention of hundreds of protesters throughout Russian Federation, including of Navalny.
Sunday amounts to "the biggest show of defiance since the 2011-2012 wave of demonstrations that rattled the Kremlin and led to harsh new laws aimed at suppressing dissent", says the AP.
Authorities in most cities, including Moscow, refused to authorize the rallies.
It also called for Russian Federation "to release without delay the peaceful demonstrators that have been detained". The foundation's report inspired numerous protesters who turned out Sunday.
"If thousands of people turn out for unsanctioned meetings in the regions, that means millions support them", Navalny said.
The Interfax news agency said 130 people were arrested in Saint Petersburg, where about 4,000 people gathered in the city center.