Moscow (CNN) -- Tens of thousands of anti-government protesters marched in Moscow on Tuesday, rejecting the legitimacy of President Vladimir Putin and demanding new elections, a prominent opposition leader said.
"We believe that his presidency right now is not legitimate at all," former Prime Minister Mikhail Kasyanov told CNN from the rally.
The elections in March that returned Putin to the presidency after four years as prime minister "were not free, they were not fair and the results were not credible," Kasyanov said.
The only thing that Putin should do now is "sit with us on a round table and discuss the terms and conditions of his departure," Kasyanov said.
International observers said in March that the elections did not meet international standards. The presidential election came just months after allegations of fraud in parliamentary elections prompted the largest anti-government demonstrations Russia had seen in two decades.
Kasyanov called for more street demonstrations to increase pressure on Putin, but said the opposition was not trying to mimic the Arab Spring.
"The best way is just peaceful protests on the streets," he said. "We would like something like what happened at the end of the '80s in eastern Europe" when Communist regimes fell without violence in the face of public dissent.
The demonstration finished without violence and with noticeably less police presence than at a protest before Putin's inauguration last month.
More than 250 people were arrested at that demonstration, including leading opposition figure Boris Nemtsov, leftist radical group leader Sergei Udaltsov and popular blogger Alexei Navalny, Moscow police told CNN.
In March, Putin won the country's presidential election with nearly 65% of the vote, claiming victory amid allegations by independent polling monitors of widespread electoral violations. International observers said there was legitimate uncertainty about the vote, with chess champion-turned opposition activist Garry Kasparov accusing Putin's supporters of "massive fraud."
Putin, the former KGB officer who has worked to both stabilize Russia's economy and curtail dissent, held the presidency for eight years before term limits forced him to step down in 2008.
CNN's Zain Verjee contributed to this report.