Russian police have arrested more than 3,000 people in nationwide protests demanding the release of opposition leader Alexey Navalny, the Kremlin’s most prominent foe.

The unprecedented demonstrations in more than 60 cities – in temperatures as low as -50 Celsius (-58 Fahrenheit) – highlighted how Navalny has built influence far beyond the political and cultural centres of Moscow and St Petersburg.

In Moscow, an estimated 15,000 demonstrators gathered in and around Pushkin Square in the city centre, where clashes with police broke out and demonstrators were dragged off by helmeted riot officers to police buses and detention trucks. Some were beaten with batons.

Navalny’s wife Yulia was among those arrested.

The protests stretched across Russia’s vast territory, from the island city of Yuzhno-Sakhalinsk north of Japan and the eastern Siberian city of Yakutsk, where temperatures plunged to -50C, to Russia’s more populous cities.

Navalny and his anti-corruption campaign have built an extensive network of support despite official government repression and being routinely ignored by state media.

Navalny was arrested on January 17 when he returned to Moscow from Germany, where he had spent five months recovering from an alleged severe nerve-agent poisoning that almost killed him, which he blamed on the Kremlin. Russian authorities have denied the accusation.

Authorities say his stay in Germany violated terms of a suspended sentence in a 2014 criminal conviction, while Navalny says the conviction was for made-up charges.