MOSCOW, March 1 - Tens of thousands of Russians marched through central Moscow on Sunday, carrying banners declaring "I am not afraid" and chanting "Russia without Putin" in memory of murdered Kremlin critic Boris Nemtsov, Reuters reported.

Nemtsov, a fighter against corruption who said he feared Russian President Vladimir Putin may want him dead, had hoped to start the opposition's revival with a march he had been planning for Sunday against Putin's economic policies and Russia's role in east Ukraine.

Ukrainian President Petro Poroshenko said Nemtsov had told him about two weeks ago that he planned to publish evidence of Russian involvement in Ukraine's separatist conflict.

The Kremlin denies sending arms or troops to Ukraine.

The authorities have suggested the opposition itself may have been behind his shooting in an attempt to create a martyr and unite the fractured movement.

His supporters have blamed the authorities.

"If we can stop the campaign of hate that's being directed at the opposition, then we have a chance to change Russia. If not, then we face the prospect of mass civil conflict," Gennady Gudkov, an opposition leader, told Reuters.

"The authorities are corrupt and don't allow any threats to them to emerge. Boris was uncomfortable for them."

Families, the old and young walked slowly, with many holding portraits of the opposition politician and former deputy prime minister who was shot dead while walking home from a nearby restaurant on Friday night.

A small but active opposition now says Putin's rule has become an autocracy that flaunts international norms after Russia seized Ukraine's Crimea peninsula last year, fanned nationalism over the separatist war in eastern Ukraine and clamped down on dissent.

"(Nemtsov) was harmful to the authorities, but the authorities themselves are criminal. The authorities have trampled on all international rights, seized Crimea, started war with Ukraine," said Yuri Voinov, an elderly physicist.

Police said 21,000 people attended the march. The organizers put the numbers at tens of thousands, but attendance appeared smaller than the 50,000 people the opposition had hoped for.

People walked in the rain within view of the Kremlin's red walls and past the spot, now covered in flowers, where Nemtsov was shot dead.

Some carried large banners carrying Nemtsov's face reading "Heroes Never Die", the same slogan used in Ukraine to celebrate more than 100 people killed in protests that overthrew Moscow-leaning President Viktor Yanukovych a year ago.

Putin has vowed to pursue those who killed Nemtsov, calling the murder a "provocation".

National investigators who answer to the Russian leader offered a 3-million-rouble reward, around $50,000, for information on Nemtsov's death. They say they are pursuing several lines of inquiry, including the possibility that Nemtsov, a Jew, was killed by radical Islamists or that the opposition killed him to blacken Putin's name.

Nemtsov's funeral is due to be held on Tuesday in Moscow. (rt/ez)