Boris Nemtsov, an outspoken critic of President Vladimir Putin and Russia's role in the Ukraine crisis, was shot dead steps from the Kremlin in a murder that underscored the risks taken by the Russian opposition.

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 in central Moscow with a Ukrainian woman, who was unhurt, just before midnight on Friday, police said.

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

A former deputy prime minister who had feared he would be murdered, Nemtsov was the most prominent opposition figure killed in Putin's 15-year rule. The Kremlin deflected blame and the government said everything must be done to find the killers.

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 have 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.

There was no immediate claim of responsibility and former Soviet President Mikhail Gorbachev cautioned against jumping to conclusions.

"Certain forces will try to use the killing to their own advantage. They are thinking how to get rid of Putin," he said.

US President Barack Obama called for a prompt, impartial and transparent investigation to ensure those responsible were 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 criticised Putin over Russia's involvement in the Ukraine crisis, said in a statement.

Opposition politicians and some foreign officials said the murder showed the problems faced by dissident voices in a country where Putin demands total loyalty.

"In Putin's atmosphere of hatred and violence, abroad and in Russia, bloodshed is the prerequisite to show loyalty, that you are on the team," another opposition leader, former world chess champion Garry Kasparov, said on Twitter.

"If Putin gave (the) order to murder Boris Nemtsov is not the point. It is Putin's dictatorship. His 24/7 propaganda about enemies of the state."

ANONYMOUS THREATS

Less than two hours after Nemtsov's death, police washed blood off the sidewalk on Great Moskvoretsky Bridge. By daybreak, flowers lay at the scene and Nemtsov's portrait had been placed beside them.

Nemtsov, who police sources said had been out walking after a meal in a restaurant by Red Square, had said in a recent interview he was concerned that the president might want him dead over his opposition to the conflict in Ukraine.

"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 opposition politician Ilya Yashin.

Sunday's opposition march is intended to 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.

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

Organisers of Sunday's march were divided after Nemtsov's death over whether to hold the rally or turn it into a demonstration of mourning in central Moscow.

OPPOSITION AT CROSSROADS

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.

Nemtsov was a fighter against corruption. In other reports, he condemned 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.

He 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.

The opposition has failed to dent Putin's popularity even though many Russians are feeling the pain of Western economic sanctions over Ukraine, low oil prices and poor economic management.

Opposition blogger Alexei Navalny is serving a 15-day jail term, preventing him attending Sunday's march in Moscow. Kasparov is based in the United States 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, was shot dead outside her Moscow apartment on Putin's birthday in 2006. The person who ordered the killing has never been identified.