Russian President Vladimir Putin has vowed to do everything possible to bring to justice those responsible for the "vile" murder of opposition politician Boris Nemtsov in a drive-by shooting near the Kremlin.

"Everything will be done so that the organisers and perpetrators of a vile and cynical murder get the punishment they deserve," Putin said in a telegram to Nemtsov's mother published on the Kremlin's website on Saturday.

Putin told Nemtsov's 86-year-old mother, Dina Eidman, that his death was an irreparable loss and that he had "left his trace in Russia's history, in politics and public life."

Nemtsov, who served as deputy prime minister under Boris Yeltsin's presidency in the 1990s, "worked in significant posts during a difficult transitional period for our country," Putin said.

"He always directly and honestly announced his position, stood up for his point of view."

Prime Minister Dmitry Medvedev also praised Nemtsov as a "principled person" who "acted openly, consistently and never betrayed his views."

He said he was "shocked at the cruel and cynical murder".

US President Barack Obama decried the "brutal" and "vicious murder" of Nemtsov, which came ahead of a major opposition rally planned for Sunday, and called on Russia to conduct an impartial probe.

French President Francois Hollande called the killing a "hateful murder" of a "defender of democracy".

A constant stream of people laid flowers and set candles at the site of the murder on Saturday morning, with police closing off one lane of traffic to let them through, an AFP reporter saw.

The Kremlin said Putin had taken personal control of the investigation.

Putin's spokesman Dmitry Peskov said the murder of the 55-year-old former deputy prime minister bore "the hallmarks of a contract killing" and described it as a provocation.

The last Soviet leader Mikhail Gorbachev, quoted by Interfax, said the killing was aimed at "destabilising the situation in the country, at heightening confrontation" with the West.

The brazen assassination was one of the highest-profile killings during Putin's 15 years in power and recalled the shooting of anti-Kremlin reporter Anna Politkovskaya, who was gunned down on Putin's birthday in 2006.

Investigators said Nemtsov was shot by unidentified assailants from a white car as he was walking with a woman along a bridge just metres (yards) from the Kremlin.

The woman was identified as Ukrainian model Anna Duritskaya by Life News website.

"According to preliminary information, an unidentified person shot at Boris Nemtsov no fewer than seven or eight times from a car as he was walking along the Bolshoi Moskvoretsky bridge," said investigators.

Interior ministry spokeswoman Yelena Alekseyeva said four bullets struck Nemtsov.