Boris Nemtsov, a 55-year-old former deputy prime minister and leading Russian liberal political figure for the past two decades, was gunned down shortly before midnight on Friday as he walked across a bridge near the Kremlin with a female companion.

The killing came just hours after a radio interview in which he called on Moscow residents to join an opposition rally on Sunday to protest Russian President Vladimir Putin's handling of the economic crisis and his "aggressive policy - deadly for our country and many citizens - of war against Ukraine."

Boris Nemtsov prepares for his interview on radio station Ekho Moskvyat on Friday (APTN)

State television on Saturday featured Russian investigators, politicians and political commentators speculating on possible reasons Nemtsov was gunned down in the heart of Moscow, but they avoided mentioning the possibility that he was murdered for his relentless opposition to Putin.

Moscow's leading investigative agency said it was looking into several possible murderers, including Islamist extremists, someone offended by his love life, and western agents trying to destabilise the political situation in the country.

Nemtsov was working on a report presenting evidence that he believed proved Russia was directly involved in the Ukraine conflict, despite official denials that it has supplied the separatists with troops and sophisticated weapons.

Boris Nemtsov addresses demonstrators during a massive rally to oppose president Vladimir Putin's policies in Ukraine on 15 March 2014 (AP)

After his death, organisers cancelled the rally and instead called for a demonstration to mourn him on Sunday in central Moscow.

The city gave quick approval, in contrast to its usual slow and grudging permission for opposition rallies.

The mourning march could serve to galvanise the beleaguered and marginalised opposition, or it could prove to be a brief catharsis after which emotions dissipate.

Popular support for Putin has remained above 80 percent in recent months, despite the severe economic recession and soaring inflation.