Russian opposition leader Alexei Navalny has appeared in court, a day after being detained at a major opposition rally which he led.

Tens of thousands of protesters took to the streets across the country on Sunday in the biggest show of defiance since the 2011-2012 anti-government protests.

The Kremlin has dismissed the opposition as a Westernised urban elite disconnected from the issues faced by the poor in Russia's far-flung regions, but Sunday's protests included demonstrations in the areas which typically produce a high vote for President Vladimir Putin, from Siberia's Chita to Dagestan's Makhachkala.

Russian police said about 500 people were arrested, while human rights groups said 1,000 were taken into custody.

On Monday, the European Union called on Russian authorities to release the detained demonstrators.

The protests were led by Navalny, a charismatic opposition leader who has recently announced his bid for the presidency.

He was seized by police while walking to a rally in Moscow from a nearby subway station.

He posted a selfie on Twitter from the courtroom on Monday morning, saying: "A time will come when we'll put them on trial too - and that time it will be fair."

If found guilty, he could be jailed for 15 days for staging an unauthorised rally.

The 40-year old, arguably Russia's most popular opposition leader, has twice been convicted of fraud and embezzlement charges which he has dismissed as politically motivated.

He is currently serving a suspended sentence, and Sunday's arrest could be used as a pretext to convert it into jail time.

Separately, police arrested 17 associates of Navalny who were at their office, setting up and monitoring a webcast of the rally.

All of them spent the night at the police station while authorities raided their office, reportedly taking out all equipment. It was not immediately clear what charges they may be facing.

Whether Navalny and his associates will be slapped with new charges could indicate which approach the Kremlin will take in dealing with a new wave of discontent - crack down on it even further or exercise restraint.