Kremlin critic Alexei Navalny was released on Friday after serving 30 days in jail for planning opposition protests, which have grown into a movement that has shaken Moscow since last month.

Police were present outside the prison on his release but made no move to re-arrest him, as they have when other opposition figures were freed recently.

Navalny emerged from jail smiling, wearing a sweatshirt and sports trousers and with a bag slung over his shoulder.

The opposition leader and anti-corruption campaigner immediately condemned "acts of terror" by Russian authorities in putting down protests in Moscow in recent weeks.

"The movement will continue to grow and the regime will strongly regret what it has done," he told journalists.

Navalny was arrested in Moscow on July 24 as he left his home to go jogging and buy flowers for his wife's birthday.

The move came as authorities sought to crush a new wave of opposition protests over the exclusion of several opposition figures, including allies of Navalny, from local Moscow polls on September 8.

As he enters his third decade in power, President Vladimir Putin's approval ratings have dropped significantly and critics say the authorities fear any outlet calling for wider political change.

Navalny, 43, a Yale-educated lawyer, was sentenced to 30 days in jail for violating laws on the organisation of demonstrations.

During his incarceration, he was treated in hospital for what doctors called a "severe allergic reaction", while Navalny said he might have been "poisoned".

Several banned demonstrations to demand free elections in Moscow have led to thousands of arrests in recent weeks in some of the largest opposition protests since Putin's return to the Kremlin in 2012.

Most of the Moscow opposition leaders are in jail, while Navalny's anti-corruption foundation has been targeted by authorities.