Thousands of Russians chanted "Russia will be free" in a march through Moscow yesterday to protest against President Vladimir Putin, shrugging off his tough new tactics intended to quash any challenge to his rule.

Protesters streamed down a leafy central boulevard in the first major rally since Putin was sworn in on May 7, saying they would not be deterred by police raids on opposition leaders' homes and a new law stiffening fines for public order offences.

"Those who fought are beyond being scared," said Valery Zagovny, a 50-year-old who served for the Soviet army in Afghanistan and wore the medals to prove it. "Let those behind the red-toothed walls of the Kremlin be scared."

Welcomed by a heavy downpour some joked had been orchestrated by Putin himself, protesters waved flags and shouted: "Russia without Putin" despite the absence of leaders who had been summoned to appear before investigators.

Leftist leader Sergei Udaltsov ignored his summons for questioning about violence at a rally on the eve of Putin's inauguration, and led a group of marchers carrying red flags and chanting "Putin to jail!" and "All power to the people!"

Ilya Ponomaryov, an opposition MP, said about 60000 to 70000 people had turned out, much higher than the police estimate of 18000.

After tolerating the biggest protests of his 12-year rule while seeking election, Putin has signalled a harsher approach to dissent since the start of his new term as president.

In power since 2000, Putin easily won a six-year term on March 4 after four years as prime minister.

His mantra of ensuring stability finds deep support among the elderly and many outside the cities, as have his strong measures against the protesters, accused by some of his backers of being spoilt urbanites financed by foreign powers.

Opposition leaders say Putin's heavy-handed tactics show that the former KGB spy is deeply worried by the protests that have undermined his once iron-clad authority.

He has signed a law increasing fines, in some cases more than 100-fold, for violations of public order at demonstrations, despite warnings from his human rights council that it was an unconstitutional infringement on free assembly.

Police and investigators raided the apartments of anti-corruption blogger Alexei Navalny and socialite Ksenia Sobchak on Monday, seizing computer drives and disks, photos and other belongings.

Many protesters are middle-class city dwellers who have benefited from the oil-fuelled boom during Putin's years in power but want more of a say in politics and fear his prolonged rule will bring economic stagnation.