Some young people were paid to attend, a presidential spokesman said.
But defiant opposition leader Alexei Navalny, one of hundreds of people held, was fined the minimum 20,000 roubles (£280; $350) and was not detained when he appeared in court.
He repeated accusations of corruption against PM Dmitry Medvedev.
The allegations were the main reason behind Sunday's protests, which drew thousands of demonstrators nationwide, including in Saint Petersburg, Vladivostok, Novosibirsk, Tomsk and several other cities, as well as Moscow. At least 500 protesters were detained.
Kremlin spokesman Dmitry Peskov, in the first comments by the presidency since the protests, said: "Essentially what we saw yesterday in several places - probably especially in Moscow - is a provocation and a lie."
He said young people had been "promised financial rewards in the event of their detention by law enforcement agencies".
Mr Peskov praised the "appropriate, highly professional and legal" response of the security forces and dismissed calls from the European Union on Monday that those detained should be released "without delay".
Asked by the BBC whether Mr Medvedev should respond to the concrete allegations of corruption which brought the crowds on to the street, Mr Peskov said: "No comment".
But he said that, where rallies had taken place legally, "in these cases obviously the slogans, the criticism that was voiced will be paid attention to".
Correspondents say the marches appear to be the biggest since anti-government demonstrations in 2011 and 2012.
What happened to Alexei Navalny in court?