Islamic extremists and the CIA are among the suspects fingered by Russian media for the murder of prominent Putin critic and Russian opposition politician Boris Nemtsov.

On Friday night former deputy prime minister Nemtsov was shot four times in the back as he crossed a Moscow bridge within sight of the Kremlin by an unidentified attacker in a car.

His murder comes after Nemtsov called for a March of Spring rally on Sunday to protest against Russia's involvement in the war in eastern Ukraine, and has led to condemnation from the international community, with US President Barack Obama calling for a "prompt, impartial and transparent investigation".

Commentators in the West argue that Putin's Kremlin is behind the slaying, in an attempt to crush dissent and intimidate the opposition.

Russian investigators though have described the murder as a "provocation aimed at destabilising the country", and Russian state media is already awash with conspiracy theories, alleging the involvement of foreign agents determined to discredit Putin and destabilise the country.

Only hours after the killing, TV station Life News quoted an unnamed source close to the investigation who said: "The purpose of the murder could be a provocation with which opponents wanted to strike at the current government. Perhaps external and internal opponents chose Nemtsov as a "victim" to contribute to the destabilisation of the situation in Russia."

The member of the 'investigation team' goes on to allege that Nemtsov may have been killed by Ukrainian backers, when he failed to implement to divide Russian society.

Claims of nefarious foreign involvement are echoed in Pravda by academic Moti Nissani, who describes Nemtsov as a "fifth columnist", and alleges that the CIA is behind the killings in an attempt to discredit Putin.

"In my view, the probability that the Russian government is behind the killing of Boris Nemtsov is close to zero, while the probability of involvement of the CIA and its allies and stooges is well over 90%," he writes.

On Russia today, investigators are reported as claiming that the murder was "carefully planned", and Islamist radicals could be responsible.

"There are reports that Nemtsov received threats due to his position over the shooting of Charlie Hebdo staff in Paris," Vladimir Markin, spokesman for the Investigative Committee, said.

In the West, experts have argued that the Kremlin is complicit in the plot.

"Just like all opposition leaders in Russia. Nothing Boris Nemtsov did was not bugged, tailed, filmed or monitored by the secret police. It is quite simply impossible that this man could have been shot dead without the Kremlin knowing there was a plot afoot to kill him," writes author Ben Judah in the Telegraph.

Other blamed Russian state media for creating a climate of hatred and paranoia towards opposition figures.

Alexei Makarkin, deputy director of the Moscow-based Centre for Political Technologies think tank, told The Moscow Times: "Anti-liberal propaganda has fostered the sense of mutual hatred in society. What we have is a situation that could detonate at any moment."

"This killing demonstrates to what extent hatred has been legitimised or even sanctioned in Russia. Society was irritated for a long time, but when the hatred comes from TV screens, it makes a big difference," he added.

The slew of rumours and innuendo surrounding Markov's death in the Russian media is ironic, as Nemtsov was a prominent critic of Kremlin propaganda.

In one of his final tweets before his murder, he wrote, '"Are you tired of lies, propaganda, war, rising prices? Then come to the March of Spring.'"