The Kremlin has responded to mass protests on Sunday by accusing the opposition of encouraging lawbreaking and provoking violence.
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?
Before his appearance on Monday, Mr Navalny, 40, tweeted from the building: "Hello everyone from Tverskoy Court. The time will come when we will have them on trial (only honestly)."
He argued it was Mr Medvedev who should be summoned as the chief organiser of the protests, because his "corrupt activities led to people coming on to the streets of 99 Russian cities".
Mr Navalny, denying all the charges, said: "They haven't heard witnesses, nor have they satisfied any of our requests. Even the slightest semblance of justice is totally absent here."
He also said again that he plans to run for president in 2018.
Mr Navalny was fined for organising banned protests but was not detained. The court could have ordered a detention of up to 15 days.
A second charge of disobeying police orders is still pending.
The BBC's Sarah Rainsford in Moscow says it is difficult for the authorities to know what to do with Mr Navalny - if he is put behind bars he becomes a martyr, if he is out then he can organise more protests on the streets.
What were the protests about?
Mr Navalny called for the nationwide protests after he published reports claiming that Mr 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 12 million times.
It includes the accusation that Mr Medvedev had a special house for a duck on one of his properties - and on Sunday, 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 Mr Navalny was hit with green liquid.
Mr Medvedev's spokeswoman called the allegations against him "propagandistic attacks".
When asked how he spent Sunday, the prime minister said simply on Instagram: "Had a good day, I went skiing", and posted a smiley face.
What have the EU and US said?
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."
What have the media said?
Russian state television completely ignored the protests on Sunday. Monday morning's bulletins were similarly blank.
Pro-Kremlin newspapers also ignored the protests.
But the BBC's Steve Rosenberg in Moscow says there was coverage in some others. Business daily Vedomosti reported a high level of dissatisfaction with the authorities, saying that the young generation had become politicised.
Another paper refers to "Putin's disastrous anniversary" - the protests coming 17 years after the president took office - and says: "A few months ago, Alexei Navalny was seen as yesterday's man who'd missed the bus. He hasn't missed any bus."
Who is Alexei Navalny?
The most prominent critic of President Putin, Mr Navalny began his anti-corruption campaign with blogs aimed at state-controlled companies in 2008.
He moved on to opposing the ruling party, United Russia, calling it the "party of crooks and thieves".
He led massive protests following the 2011 election, the biggest in Moscow in December that year, after which he was arrested and jailed for 15 days.
He has said he will run for president in 2018, but a court has convicted him of embezzlement, which would bar him. He denies the charges, calling the case farcical.