The letter calls for efforts to resolve the crisis in eastern Ukraine, which threatens the "possibility for a peaceful life for over 800 million Europeans".
The letter also warns about the fracturing of Europe and claims that the "trade and economic sanction duel" along with the recent events in Paris threaten the safety of the European continent.
The letter was translated to Swedish and dated for the end of January, but newspaper Svenska Dagbladet claims that it was sent more recently to Swedish and European politicians.
Liudmila Klimenkova, a press attaché at the Russian Embassy in Stockholm, confirmed that Russia had sent the letter, but the embassy would not give any further comments.
Björn Palmertz, an analyst at the Swedish Defence University, said that while he had not completed an analysis of the letter, he did not necessarily see it as a threat.
"It's in line with Russia's aggressive behavior in the information sphere, and it's a line we have seen in practice before," Palmertz told Svenska Dagbladet.
"One highlights the common heritage [with Europe], saying that one is prepared to work together, but without taking up Russia's own actions in the Ukraine. And one emphasizes that the recipients of the letter have a political responsibility to ensure that the whole thing that does not evolve into further conflict," Palmertz said.