Tens of thousands of people marched in central Moscow on Sunday afternoon to honour the memory of the murdered Russian opposition politician Boris Nemtsov.

Moscow police said some 21,000 people took part in the march. The organisers put the turnout at tens of thousands.

Opposition supporters gathered at a point not far from the Kremlin. The march then proceeded to the spot on Great Moskvoretsky Bridge where Nemtsov was shot dead on Friday.

People walked in silence, carrying Nemtsov's portraits and placards reading “Heroes never die”, “He fought for a free Russia” and “He fought for our future”. Many were carrying the Russian national flag and flowers to lay at the site of the assassination just right next to the Kremlin.

Smaller marches in memory of the outspoken critic of Russian President Vladimir Putin were also held in several other Russian cities, including St Petersburg, Voronezh, Yekaterinburg and Tomsk.

Reuters quoted opposition leader Gennady Gudkov as saying before the march: "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."

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

At the time of his death Nemtsov was believed to be working on a study detailing the suspected presence of Russian troops in Ukraine - a claim the Kremlin has persistently denied.

National investigators, who are reporting directly to Putin, offered a reward of three million roubles (USD 50,000) for information on Nemtsov's death.

Hours before he was gunned down, Nemtsov had broadcast a radio appeal to supporters to join him at a rally on Sunday in Moscow to protest against the Kremlin’s involvement in Ukraine and demand an immediate end to the conflict there.

The protest instead was turned into a Nemtsov memorial march.