More than a thousand opposition activists of various stripes marched in central Moscow on Sunday after President Vladimir Putin proposed re-drafting the constitution, unleashing political upheaval.

Protesters -- mostly young anti-fascist activists -- chanted "Revolution" and "No to dictatorship" and some carried copies of the constitution.

The annual sanctioned march was called to commemorate the memory of lawyer Stanislav Markelov and journalist Anastasia Baburova who were gunned down in Moscow by ultra-nationalists in 2009.

A number of independent local deputies including Yulia Galyamina and opposition-minded Russians joined the march, carrying copies of the constitution and chanting "Putin leave!".

About ten people including a protester who carried a placard urging Putin to quit power were detained by police.

Pyotr Alyoshin, a 54-year-old lawyer, said at the march he was against changing the country's basic law.

"The constitution that I hold in my hands protects our rights and basic freedoms," he told AFP.

Galyamina, who had earlier said it was important to protest against Putin's attempts to cling to power and urged ordinary people to join the march, acknowledged the meagre turnout but said average Russians were confused.

"We will explain it to them," she told AFP. "I think people will be joining the fight to prevent a state coup in Russia."

More than 1,400 people took part in the march, said the White Counter group which monitors political protests.

The march wasn't supposed to be about Putin, but many had a go at him anyway
The march wasn't supposed to be about Putin, but many had a go at him anyway AFP / Alexander NEMENOV

The march took place after Putin stunned the nation on Wednesday by proposing sweeping amendments to the constitution, the first major changes to the country's basic law since it was adopted under Boris Yeltsin in 1993.

The move triggered the resignation of his government.

Observers say Putin's proposals are designed to ensure his grip on power after he leaves the Kremlin and his critics have accused him of orchestrating a "constitutional coup".

But Sunday's turnout paled in comparison to the protests of last summer when tens of thousands took to Moscow's streets to protest against the exclusion of opposition candidates from local elections, leading to wide-scale arrests and long jail terms for a number of demonstrators.

Russia's top opposition leader Alexei Navalny said on Friday he did not support rallies in "defence of the constitution".

"The Russian constitution is abominable," he said on Twitter, adding it allowed authorities to usurp power. "No need to protect it."

Political analysts Kirill Rogov criticised Navalny, saying his words betrayed "fatigue" and that the constitution was a "set of ideas" and was therefore worth fighting for.

Observers say Putin's proposals have caught Kremlin critics off guard and managed to drive a new wedge between members of the Russian opposition.

"Russian society is entering the 2020s extremely atomised, and the Kremlin will certainly be able to use it," said independent newspaper Novaya Gazeta.