Thousands of people turned out in more than 180 cities across Russia, according to Navalny's campaign headquarters, which would make it the most widespread protest in the country since Vladimir Putin returned to the presidency in 2012.
But Putin's spokesman, Dmitry Peskov, played down the notion of any risk to the government.
"Whenever such events are held according to agreed-upon rules, as prescribed by law, they do not pose a danger to anyone," he said in remarks carried by the Interfax news agency. "Some are attended by more people and some are by less, but this is a normal process of people expressing their opinions as citizens."
The Interfax report did not include a reference to Navalny but quoted Peskov as condemning the "group of provocateurs" who interrupted the celebration of the national holiday.
Peskov also dismissed a sharply worded statement read by White House press secretary Sean Spicer on Monday night, declaring that "detaining peaceful protesters, human rights observers and journalists is an affront to core democratic values."
Peskov countered that authorized rallies went off peacefully in dozens of Russian cities Monday and that those "who staged provocations" had been dealt with lawfully.
Pollsters say that Putin, who has enjoyed an approval rating above 80 percent for more than three years, is likely to win if he runs for a new six-year term in March, as expected. Even though he presides largely unchecked over a government and legislature led by his handpicked loyalists, most Russians do not blame the president for their problems, according to surveys conducted by the country's independent pollster, the Levada Center.
But many do count on Putin to solve their problems. Two days before his annual televised "direct line" with citizens, 1.3 million Russians had submitted questions, the official Tass news agency reported Tuesday.
The telethon's official website displayed some of the appeals, which beseeched Putin to address the poor state of roads, housing, construction projects, the mortgage market, education and the accountability of officials. One young man asked why so many young Russians want to emigrate. Several asked Putin to explain why the rest of the world fears Russia.
Navalny, meanwhile, promises Russians a rule-of-law state governed by honest people, contrasting that with his allegations of corruption in Putin's government. That message has yielded little support, with polls indicating that less than 10 percent of voters would choose Navalny.
And there is no guarantee Navalny will be allowed to run: He can be disqualified, thanks to a conviction in a fraud case he says was politically motivated.
Late Monday, Navalny posted a video from the courtroom where he was sentenced. He thanked his supporters and told them, "I'm proud to be part of the movement."
Meanwhile, pro-Kremlin media blasted Navalny's decision to move his rally to central Tverskaya Street as a cynical ploy to capitalize on holiday events in the city, including a huge concert in Red Square.
"Why did the opposition do this? Only to provide pictures for Western television companies so that they could say, 'In Moscow, President Putin has opponents!' " stated a commentary in the official government newspaper, Rossiyskaya Gazeta. "The opposition, which represents one-thousandth of the population of Muscovites, tried to turn all of Tverskaya Street into a film studio and pass off the people celebrating Russia Day as their supporters."