Itar-Tass, citing a source in the Conservative Prime Minister's office, said Britain was "extremely interested" in referendum support from Russia, which this year holds the presidency of the influential G8 group of rich industrial nations.
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The state-owned agency - acknowledged as the Kremlin's official mouthpiece before and after the end of Communism - said the Cameron aide had warned Scottish independence could "send shockwaves across the whole of Europe".
Its report, which follows claims Cameron and his Spanish counterpart Mariano Rajoy have forged an "anti-separatist pact", sparked criticism last night from Alex Salmond.
The First Minister said: "This report from Russia raises serious questions about the UK Government's underhand tactics. If this is accurate, then Westminster has been caught red-handed trying to stir up hostility to Scotland instead of representing Scotland's interests - it seems the No Campaign's self-named 'Project Fear' has now gone global."
The Scottish Government, as revealed in this newspaper, has already launched its own diplomatic charm offensive, trying to explain its independence project to sceptical governments such as Rajoy's.
For the first time since devolution an Edinburgh administration is pursuing a foreign policy that is at odds with the interests of the British state.
However, some nationalists increasingly suspect that Whitehall is using diplomatic back channels to rubbish independence.
The Tass report, by one of the agency's correspondents, hit the Russian language news wires on Hogmanay.
Its opening paragraph reads: "Great Britain is extremely interested in the support of Russia, as holder of the G8 presidency, in two vital areas in 2014: the Afghan pull-out and the Scottish independence referendum."
In the traditional style of a Russian news wire report, this assertion was then attributed to a "representative" in the Prime Minister's office who was speaking anonymously.
The journalist then added a direct quote from the unnamed source talking of "two main issues whose resolution requires international formats, albeit of different modalities".
The Cameron Government insider then, according to the report, added: "Those are the withdrawal of combat units from Afghanistan by the end of the 2014 and September's referendum on Scottish independence.
"We believe that the G8 could become one of the main political platforms where London will find backing."
The journalist added that although the referendum might "look like a UK domestic matter", it had, according to his UK Government source, the potential to "send shockwaves across the whole of Europe".
David Cameron is understood to have recently tried to repair his relationship with Putin, especially with the Russians set to chair a summit of G8 and EU leaders in the Black Sea resort of Sochi this June.
The Tass report mostly focused on this. London, it said, was hoping for "special relations" with Moscow in the run-up to Sochi. "We are eager for G8 consultations with Russia," the representative from Cameron's office was quoted as saying.
The summit will see the leaders of France, the United States, Canada and Russia - all thought to be hostile to Scottish independence - gather in one place just three months before the Scottish vote.
Few international leaders have spoken out in public about the Scottish referendum.
The only major figure to buck this trend is Spain's Rajoy, who late last year announced that Scotland would be "outside the EU" if it voted for independence.
Madrid's El Pais newspaper reported that Rajoy had met Cameron to "consult" on independence movements in Scotland and Catalonia, whose government hopes to hold its own referendum shortly after Scotland's.
The paper said the Spanish premier was seeking "British complicity" in his bid to stop Catalans breaking away.
A Number 10 source, asked about the meeting which was in Vilnius, Lithuania, later said: "We don't recognise talk of a deal."
Last month, this newspaper revealed two senior Downing Street officials, including Cameron's adviser on Scotland, Andrew Dunlop, had flown to Madrid at the invitation of Rajoy's ultra-unionist and conservative administration.
Salmond, in response, accused Cameron and Rajoy of working "hand in glove". Scottish Tories dismissed the suggestion and accused the First Minister of "childish rhetoric".
The UK Government dismissed the visit as routine.
Russian state media, meanwhile, has recently issued numerous dire warnings about the "epidemic of separatism" infecting both Scotland and Catalonia.
Putin has effectively run the Kremlin since 1999, either as prime minister or president, on a strongman policy of securing Russia's "territorial integrity".
Salmond said: "It is shameful that as Prime Minister David Cameron refuses to debate in front of the people of Scotland, but is perfectly willing to lobby against Scotland's
interests around the world. This adds credibility to reports the Prime Minister was lobbying the Spanish prime minister to make comments against Scottish independence when their foreign minister had already made perfectly clear that Scotland's referendum is a matter for the people of Scotland.
"This kind of behaviour shows exactly why Scotland should represent our own interests as an independent nation.
"We will be a responsible global citizen and a good friend to our neighbours in the rest of the UK."
Patrick Harvie MSP, the joint convener of the Scottish Greens, said: "If accurate, these extraordinary comments show a deeper sense of misjudgement than I thought the UK Government was capable of.
"The one thing I thought even the Cameron government accepted was that the referendum is for the Scottish people to settle, so why they feel the need to court the support of Vladimir Putin's brutal regime I cannot imagine."
A spokesman for Cameron declined to comment, on the basis that there were "no quotes" from the unnamed representative claiming that the UK wanted Russia's support.
The Russian Embassy in London did not respond to a request for comment.