Monday's rallies were the second mass action called by Navalny since March 26.
Moscow City Hall labelled the decision a "provocation" while the police warned that a different event was being held at Tverskaya and that the protest would clash with festivities.
Navalny, who had a green liquid thrown in his face in April, robbing him of some of his sight, said hundreds of people had also attended demonstrations in Russia's Far East on Monday morning.
Protest organizers estimated 4,000 participants in the southwestern Siberian city of Omsk, and 2,000 in Irkutsk, in eastern Siberia, though the police estimates were less than half of those totals.
State media ignored the demonstrations, broadcasting Soviet-style coverage of Putin handing out state awards instead. Spicer called on the Russian government to immediately release all peaceful protesters.
Navalny argues that he was forced to call people to another unauthorised rally, claiming that no firm would supply a stage, screens or speakers for the protest he had been given permission for. The demonstrators are demanding an end to corruption they say is endemic among government officials.
Reuters reporters saw a heavy police presence on and around the avenue with bus loads of riot police parked nearby and side roads blocked off.
Why was Alexey Navalny arrested?
Navalny said protesters had a constitutional right to gather to express their political opinions and that Tverskaya Street would be an ideal location because it will be turned into a pedestrian zone for the Russia Day celebrations.
"I want to protest against corruption and the fact that the authorities are not fighting it", said Alexander, an 18-year-old student brandishing the Russian flag.
But the unsanctioned rallies were raided by riot police and more than 1000 people were rounded up by officers across the country. While they did report on the arrest of Navalny, they remained silent on the protests in the streets.
By calling crowds into the very centre of Moscow, Alexei Navalny has set the stage for a confrontation.
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It was an Iranian-made Shahed 129 and was thought to be armed and in firing range of United States troops. Military officials who spoke to CNN described it as a Shahed 129 , a model unveiled by Iran in 2012.
Police arrested the populist leader of the movement, Alexei Navalny, outside of his home before he could go anywhere.
Prominent opposition leader Alexei Navalny and around 250 others were arrested on Monday in anti-corruption demonstrations across the country, the media reported. Arrests continued in the capital throughout the afternoon.
Police say Navalny was detained for breaking laws regarding public meetings and obeying authorities, the Interfax news agency reports.
Monday's protests were a follow up to the March 26 rallies in which tens of thousands of demonstrators took to the streets in cities and towns across Russian Federation.
Petersburg and other Russian cities on Sunday, people took to the streets to speak out against corruption and President Vladimir Putin in one of the largest protests in years. People shouted "Putin is a thief" and "Russia without Putin" before being dragged away by police.
Russian opposition leader is seen getting into a police auto as he was detained in front of his home on Monday.
Navalny was arrested at his block of flats before he could even make his way to the protest.
The protests on Monday were sort of a litmus test to check if Navalny still enjoyed public support or the protest in March was an impulsive reaction that fizzled out.
There was no immediate comment from police on why Navalny had been arrested or where he was taken.
There were also supposedly permits for protests in 169 locations.
Thousands of anti-government activists challenging President Vladimir Putin's rule were protesting across Russian Federation on Monday, with police arresting main opposition leader Alexei Navalny outside his Moscow home before he could reach the main demonstration.
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