Tens of thousands of people marched in central Moscow March 1 to honour the memory of opposition leader Boris Nemtsov, who was shot dead near the Kremlin just a day before the planned Peace March in Moscow.

The event appeared the largest opposition gathering since anti-Kremlin rallies in 2011-12 brought more than 100,000 people into the streets.

Holding Russian, Ukrainain flags and Nemtsov portraits, activists marched from Moscow square to the bridge over the Moskva where Nemtsov was killed.

People held banners which read "These bullets are for each of us," "I am Boris", "I am not afraid", "Propaganda kills" and "Stop the war in Ukraine”.

US Secretary of State John Kerry, meanwhile, urged Russia to carry out a "thorough, transparent, real investigation not just (into) who actually fired the shots, but who if anyone may have ordered or instructed this or been behind this".

Around 6,000 people, some wrapped in Ukrainian flags, also turned out in Russia's second city, Saint Petersburg.

Hours before the killing, Nemtsov went on radio to urge Russians to join him at a Sunday rally in Moscow to protest against the Ukraine war and Putin's rule.

After his murder the protest was turned into a memorial march, with authorities approving a turnout of 50,000.