Russian opposition politician Boris Nemtsov, an outspoken critic of President Vladimir Putin and Russia's involvement in the war in Ukraine, was shot dead steps from the Kremlin in central Moscow late on Friday.

Nemtsov, 55, was shot four times in the back by assailants in a white car as he walked across a bridge over the Moskva River with a Ukrainian woman who was unhurt.

Police cars sealed off the blood-stained bridge close to the red walls of the Kremlin and Red Square, after a gangland-style killing reminiscent of Russia in the chaotic 1990s after the collapse of the Communist Soviet Union.

Nemtsov was by far the most prominent opposition figure killed in Russia under Putin's 15-year-rule and the Kremlin swiftly sought to deflect any blame for the murder.

Putin condemned the "brutal" slaying and took the investigation under presidential control, saying it could have been a contract killing and a "provocation" on the eve of a big opposition protest Nemtsov had been due to lead on Sunday.

But the killing focused attention on the tough treatment of Kremlin opponents in Putin's third term, during which several leading critics have been jailed or fled the country following mass rallies against the former KGB spy three years ago.

"That a leader of the opposition could be shot beside the walls of the Kremlin is beyond imagination. There can be only one version: that he was shot for telling the truth," Mikhail Kasyanov, an opposition leader and a former prime minister under Putin, said at the scene.

US President Barack Obama called for a prompt, impartial and transparent investigation to ensure those responsible are brought to justice for the "vicious killing."

"Nemtsov was a tireless advocate for his country, seeking for his fellow Russian citizens the rights to which all people are entitled," Obama, who has fiercely criticized Putin over the Ukraine crisis, said in a statement.

"I admired Nemtsov’s courageous dedication to the struggle against corruption in Russia and appreciated his willingness to share his candid views with me when we met in Moscow in 2009," he added.

He called him a "dedicated and eloquent" defender of Russians' rights.

Ed Joyce, the Republican chairman of the US House of Representatives Foreign Affairs Committee, said "lawlessness now pervades Putin’s Russia".

"Regardless of who killed Boris Nemtsov, this shocking murder is the latest assault on those who dare to oppose the Putin regime," he said.

Less than two hours after his death, police were washing blood off the sidewalk on Great Moskvoretsky Bridge as supporters were leaving flowers near where Nemtsov had fallen.

Nemtsov, who Tass news agency said had been out walking after a meal in a restaurant by Red Square, had been quoted as saying he was concerned that the president might want him dead over his opposition to the conflict in Ukraine.

Sunday's opposition march is intended as a protest against the war in east Ukraine, where pro-Russian rebels have seized a swathe of territory. Kiev, the West and some Russians accuse Moscow of sending troops to support the rebels, an accusation Russia has repeatedly denied.

"Those who are for ending Russia's war with Ukraine, for ending Putin's aggression, come to the Spring March in Maryno (Moscow) on March 1," Nemtsov said in one of his last comments for the liberal radio station Ekho Moskvy this week.

Tall, with a mop of black curly black hair that had started to turn gray, he often dressed casually in big sweaters and was known for booming speeches criticizing Putin at rallies.

Organizers of the Spring March were at odds after Nemtsov's death over whether to hold the rally he spent weeks preparing, or turn it into a demonstration of mourning in central Moscow.

Fellow opposition politician Ilya Yashin said that Nemtsov had been receiving threats before his death.

"Boris periodically received anonymous threats on social networking sites... Boris was worried. He said he was under threat but never wanted additional security. (He said) if they want to kill (me) they will kill (me)," said Yashin.

"This is a political killing which carries the characteristics of an ordered killing. The murder is connected with Boris’ opposition activities. They killed one of the brightest members of the Russian opposition to intimidate and strike fear," Yashin told Interfax news agency.

Nemtsov's criticism of Putin won him support among Moscow intellectuals and the nascent middle class but he had little support outside the big cities.

Another opposition figure, Ksenia Sobchak, said Nemtsov had been preparing a report on the presence of Russian troops in Ukraine. The Kremlin denies allegations by Kiev and Western governments that it has sent troops and advanced weaponry to back the rebels.

Like other opposition leaders, Nemtsov was a fighter against corruption. In other reports, he condemned massive overspending on the 2014 Sochi Winter Olympics by the Russian authorities and listed the many state buildings, helicopters and planes that Putin has at his disposal.

Nemtsov was also one of the leaders of the rallies in the winter of 2011-12 that became the biggest protests against Putin since he first rose to power in 2000.

Nemtsov briefly served as a deputy prime minister under President Boris Yeltsin in the late 1990s, when he gained a reputation as a leading liberal economic reformer.

However, the killing could swell attendance at Sunday's march and galvanise the opposition in a country where many people are feeling the pain of Western economic sanctions over Ukraine, the lower oil price and poor economic management.

With many leaders absent or in jail, the opposition has failed to dent Putin's popularity. Opposition blogger Alexei Navalny is serving a 15-day jail term, preventing him attending Sunday's march in Moscow.

Former world chess champion Garry Kasparov is based in the US and former oil tycoon Mikhail Khodorkovsky, freed in late 2013 after a decade in jail, lives in Switzerland.

Some opponents say they fear for their life. Anna Politkovskaya, an investigative journalist and Putin critic, was shot dead outside her Moscow apartment in 2006. Paul Klebnikov, an investigative US journalist, was shot dead in 2004.-Reuters