Up to 20,000 demonstrators have gathered in central Moscow to demand Vladimir Putin's resignation and protest against electoral fraud.

The rally is being widely seen as a test of whether the opposition is able to maintain its strength after Putin won a return to the Kremlin on Sunday amid global accusations of vote-rigging.

Putin took 64% of the vote, according to official figures, and is set to stay in the Kremlin for the next six years.

Organisers had hoped at least 50,000 people would turn out for the protest on New Arbat, one of Moscow's main streets, but independent witnesses estimated the crowd to be around 20,000.

The rally was approved by the city authorities and police were out in force, with at least two helicopters hovering overhead.

Protest leaders addressed the crowd from a stage bearing the slogans "For new elections" and "These are not elections, this is not a president".

"These authorities are illegitimate," Vladimir Ryzhkov, an opposition leader and protest organiser, told the crowd.

Protesters, in bright sunshine, waved flags, balloons and banners and wore white ribbons, the symbol of protests that began three months ago.

Although anger at Putin's re-election remains high – international observers said the vote was marred by fraud and a lack of competition – there is recognition among protest leaders that the movement must grow beyond public rallies in its bid to challenge Russia's political system.

Putin won almost two-thirds of the vote across the country but failed to break the 50% barrier in Moscow. Alexey Navalny, a popular opposition leader, has spoken of creating a "universal propaganda machine" to break the hold of state-run television in provincial Russia.

"Now is the time for long-term goals," Yevgeniya Chirikova, an opposition leader who came to prominence after fighting against the building of a road through Moscow's only oak forest, said.

"More than anything, we must go out and meet people, bring the truth to them and explain what is going on."

"Our task now is to help people realise that civil society work must be like their regular work. Of course it's hard – it takes time from your family, affects your health – but without it we will achieve nothing. We have no political competition."

Other activists, rather than seeking to spread the word beyond Moscow, are hoping to change things in the capital.

Sergei Parkhomenko, a journalist and protest organiser, said he would focus his efforts on returning mayoral elections, cancelled by Putin in 2004, to the capital.

"I want to see a battle for Moscow," Parkhomenko said, echoing Putin's pre-electoral phrase. "But not the kind that Putin has talked about – a brutal, violent one. Moscow is the only city in the country where Putin doesn't have a majority: we need to capitalise on that."