MOSCOW: Tens of thousands of people marched in central Moscow on Sunday to honour the memory of opposition leader Boris Nemtsov, who was gunned down near the Kremlin in the highest-profile assassination of Vladimir Putin's rule.

A sea of supporters, many waving Russian flags and banners, packed a Moscow square under gray skies before heading to the bridge where the 55-year-old opposition figure was shot in the back shortly before midnight Friday.

“He died for Russia's future”, “He fought for a free Russia,” some of the banners said.

Organisers said 70,000 people had turned out while police estimated the crowd at more than 16,000.

Another 6,000 people, some wrapped in Ukrainian flags, turned out to protest in Russia's second city, Saint Petersburg.

“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.

Hours before the drive-by killing, Nemtsov had broadcast a radio appeal to supporters to join him at a rally Sunday in Moscow to protest against the Kremlin's Ukraine stance and demand an immediate end to the war there.

The protest instead was turned into a Nemtsov memorial march, with Moscow authorities approving a turnout of 50,000.

'These bullets are for us'

Putin on Saturday vowed to punish the killers as Russian oppposition figures denounced what they called a “political murder” and Western leaders called for a full probe.

Nemtsov, a vocal critic of the government and a former deputy premier in the 1990s under Boris Yeltsin, died after being hit with four bullets to the back while crossing a bridge a stone's throw from the Kremlin, in sight of the golden domes of Saint Basil's Cathedral.

A woman with him on the bridge was not hurt.

The spot where he fell was heaped with flowers, candles and notes. “These bullets are for each of us,” said organisers of the memorial event.

As small memorial rallies took place in cities such as Yekaterinburg in the Urals and Tomsk in Siberia, in Voronezh, south of the capital, supporters holding signs saying “I am Boris” were attacked by pro-Kremlin activists hurling disinfectant at them.

Putin on Saturday denounced the brazen shooting as “a provocation” by political foes, while investigators said the assassination appeared to have been meticulously planned.

The Investigative Committee, which reports directly to Putin, said Nemtsov “might have been sacrificed” to sow instability, and that they were also checking any links to the Ukraine conflict.

'New epoch'

Kremlin critics said the murder of a prominent politician who had held senior government posts marked a watershed moment.

“We have entered a new epoch -- the epoch of the physical liquidation of political opponents of the regime,” said prominent commentator Yulia Latynina.

"The message is absolutely clear: anyone who attends an opposition march can be killed. This is an act of political terror."

But Putin's spokesman Dmitry Peskov sought to counter talk of the Kremlin toughening its efforts to stifle critics. “It would be too emotional and wrong to conclude that a string of such murders has begun,” he said

However some Russians said that failing direct involvement, the Kremlin bore responsibility for whipping up a climate of anti-Western hysteria and hatred against dissenters opening the way to acts of violence.

Last weekend for instance tens of thousands of Kremlin supporters including bikers and ex soldiers were called to demonstrate near the Kremlin to protect Putin from "Russia's enemies."

Tensions with the West over Ukraine and the takeover of Crimea have increasingly polarised Russian society, with most Russians behind Putin but a minority in sharp disagreement.

Nemtsov, a hate figure for pro-Kremlin activists, had long complained of being followed and having his phone tapped. In 2011, assailants mangled his Range Rover by throwing a toilet bowl on its roof.

The leader of Russia's beleagured opposition movement, Alexei Navalny, who had planned the original rally with Nemtsov, said he was “at a loss for words. “Jailed for two weeks in a move, Navalny asked authorities to allow him to bid farewell to his ally.

'Bridge between Russia and West'

Nemtsov was a former physicist who became governor of the central region of Nizhny Novgorod at 32 before serving in Yeltsin's team in the 1990s. After leaving parliament in 2003, he led several opposition parties.

A passionate orator with a ready smile and a mop of wavy black hair, Nemtsov was known for his zest for life and popularity with women.

He was a key speaker at rallies against Putin's return to the presidency in 2012 and authored reports critical of corruption and misspending under Putin.

At the time of his death he was believed to be working on a study detailing the presence of Russian troops in Ukraine, a claim the Kremlin still denies.

President Barack Obama condemned the “vicious murder” of the politician he had met on a visit to Moscow.

British Prime Minister David Cameron said the “callous murder” must be investigated “rapidly and transparently.

“Ukrainian President Petro Poroshenko called Nemtsov a “bridge between Ukraine and Russia”.

“The murderers' shot has destroyed it,” he said on Facebook.