Tens of thousands of people have marched in central Moscow to honour the memory of opposition leader Boris Nemtsov, who was gunned down at the weekend.

The 55-year-old, a prominent critic of president Vladimir Putin, was shot four times in the back on Friday night as he crossed a bridge over the Moskva river within sight of the Kremlin.

On Sunday sea of grim-faced supporters waving Russian flags with black ribbons marched in drizzle from a packed Moscow square to the bridge where Mr Nemtsov was shot.

The rally had been called by Mr Nemtsov before his death as a protest against the war in Ukraine and Mr Putin's rule.

In what appeared to be the largest opposition gathering since anti-Kremlin rallies in 2011-12, marchers honoured Mr Nemtsov's memory while slamming Moscow's stance on Ukraine.

"These bullets are for each of us," read a huge banner at the head of the march, while others stated "I am Boris", "I am not afraid" and "Propaganda kills".

"Stop the war" in Ukraine, said others.

Organisers said 70,000 people turned out, while police estimated the crowd at 21,000.

Marching with his young son, engineer Alexander Akulin dubbed Mr Nemtsov's death a "political murder".

"Political terror will intensify now," he said.

Mr Nemtsov was shot dead shortly after giving a radio interview in which he delivered a stinging criticism of the "murderous and insane" war in Ukraine, and called Mr Putin "a pathological liar".

"[Nemtsov] was a good man," said one marcher. "He was telling the truth and he was killed for the truth. And it was the Kremlin authorities who did it. And we came to express our dismay."

There is no shortage of people pointing the finger of blame at the Kremlin, including former world chess champion Garry Kasparov.

"Whether he gave a direct order, I don't know, probably will never know. But definitely the atmosphere in the country, with 24/7 propaganda, hatred, where people who disagree with Putin have been portrayed as national traitors, fifth columnists, enemies of the state... Boris was one of the formidable critics of Putin's regime."

"If we can stop the campaign of hate that's being directed at the opposition, then we have a chance to change Russia," Gennady Gudkov, an opposition leader, said ahead of the march.

"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."

Thousands march in central Moscow to commemorate Kremlin critic Boris Nemtsov. ( Reuters: Maxim Zmeyev )

Marchers also paid tribute to Mr Nemtsov in St Petersburg, where 6,000 people, some carrying Ukrainian flags, turned out.

"I am carrying a Ukrainian flag because he fought for the end of the Ukraine war. And they killed him because of that," said marcher Vsevolod Nelayev.

Mr Nemtsov was also honoured in eastern European cities including Warsaw and Budapest.

Four hundred people marched in Lithuania's capital, Vilnius, while dozens gathered on Kiev's iconic Independence Square, the focal point of Ukraine's uprising a year ago.

But in a move that worried the Ukraine authorities, Moscow police detained a Ukrainian MP Alexei Goncharenko over his alleged involvement in deadly riots in Odessa last year.

He is the second Ukrainian lawmaker held in Russia.

Mr Nemtsov, an anti-corruption crusader and vocal critic of the government, was a former deputy premier in the 1990s under Boris Yeltsin.

The spot where he fell has been heaped with flowers, candles and notes.

Mr Putin has vowed to punish the killers, calling Mr Nemtsov's murder "vile and cynical".

Western leaders have called for a full investigation.

Russia's Investigative Committee, which reports directly to Mr Putin, said Mr Nemtsov "might have been sacrificed" to sow instability, and said it was also checking any links to the Ukraine conflict.

People hold flags and posters during the march in central Moscow. ( Reuters: Maxim Shemetov )

ABC/AFP