Around 10,000 people gathered for a peaceful rally in the city centre after the Moscow election commission released the final tally showing that an ally of President Vladimir Putin, incumbent mayor Sergei Sobyanin, had scraped through in the first round with 51.3 per cent of the vote.
In a major surprise, Navalny, a charismatic 37-year-old leader of the opposition movement who campaigned under the shadow of a controversial conviction for embezzlement, polled far more strongly than projected with over 27.2 per cent.
Yet Navalny contended that the results were falsified and urged the authorities to hold a recount that he said would lead to a second-round runoff.
The rally took place on a central Moscow square, which was the focal point of huge anti-Putin protests in the winter of 2011-12 that saw Navalny become the star speaker.
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Dmitry Yagodkin, 42, said he turned up for the rally because he believed the authorities had manipulated the results.
"A second round would be a victory," said Alexander Koidan, a 21-year-old law student.
Detective novelist Boris Akunin called on Sobyanin to come out to the protesters and explain himself.
"Like many people, I have a lot of suspicions about the results of the Moscow elections," he said at the rally, interviewed by TV Rain.
The Moscow authorities had given Navalny permission to hold a rally of no more than 2,500 people.
Today evening, police said more than 9,000 people had gathered and Navalny's campaign said they had been fined for breaching the limit.
"I don't plan to let you down or put you in danger," he said.