Supporters of opposition leader Alexei Navalny are rallying across Russia, heeding his call to push authorities to let him enter the presidential race.

The wave of demonstrations on the 65th birthday of President Vladimir Putin comes as Mr Navalny serves a 20-day jail term for calling for an unsanctioned protest.

His headquarters said protests would be held in nearly 80 Russian cities. Rallies numbering from a few dozen to a few hundred people were held in several cities in Russia’s far east and Siberia.

Demonstrators wave Russian flags during a rally in MoscowDemonstrators wave Russian flags during a rally in Moscow (Alexander Zemlianichenko/AP)

Most of the demonstrations have not been sanctioned by authorities, and police detained a few protesters and activists in some cities.

In Moscow, several hundred protesters, most of them young, gathered in Pushkinskaya Square, waving Russian flags and chanting “Russia will be free!” and “Free Navalny!”

Police warned the demonstrators that the rally has not been sanctioned and urged them to disperse, but did not immediately move to break up the protest.

Police and the National Guard showed up in full force in central Moscow and in St Petersburg, where a rally is set to be held later.

Mr Navalny has declared his intention to run for president in the March election, even though a criminal conviction he calls politically motivated bars him from running.

Demonstrators carry the Russian flag during a rally in MoscowAlexei Navalny has worked to organise protests in support of his presidential bid (AP Photo/Ivan Sekretarev)

The 41-year-old anti-corruption crusader has organised several waves of protests this year, casting a challenge to the Kremlin.

Mr Putin has not yet announced his intention to seek re-election, but he is widely expected to run. With his current approval ratings topping 80%, he is set to win another six-year term in a race against torpid veterans of past election campaigns, like Communist Party chief Gennady Zyuganov.

Mr Navalny argued that a high level of support for Mr Putin results from the lack of real political competition and urged his supporters to help him get registered for the race.

“The 86% approval rating exists in a political vacuum,” he said. “It’s like asking a person who has been fed with rutabaga through his entire life how eatable they find it and the rating will be quite high. Listen, there are other things which are better than rutabaga.”

The sarcastic analogy demonstrated his stinging style, which has recently helped him get broad support among youths. He has worked to expand his reach with videos exposing official corruption and YouTube live broadcasts.

His documentary about prime minister Dmitry Medvedev’s alleged ill-gotten wealth has been viewed nearly 25 million times since its release in early March, helping galvanise protests.

Heeding his call, tens of thousands took to the streets in dozens of cities and towns across Russia in March and June, the biggest show of defiance since 2011-12 anti-government protests.