President Vladimir Putin, a former KGB spy who is poised to win a fourth term in an election on Sunday, has so far only said publicly that Britain should get to the bottom of what has happened.
"We have never encountered this level of discussion on the global stage", Peskov told reporters.
As the worldwide scandal gathers pace, Skripal and his daughter remain in critical condition after exposure to the Soviet-designed chemical Novichok on March 4 in the southwestern English city of Salisbury. "The whole wave (of such statements) originated from Britain", the state-run RIA news agency quoted Dmitry Peskov as saying.
U.S., Germany and France issue statement of solidarity, saying they agree with United Kingdom assessment that Russia was responsible for nerve agent attack on former Russian spy Sergei Skripal and his daughter.
The Foreign Secretary was speaking during a visit to the Battle of Britain Bunker museum in his Uxbridge constituency with his Polish counterpart Jacek Czaputowicz, who said: "We are sure that it is the Russian state which is involved in this attempt".
"That is why we are at odds with Russian Federation".
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Russian Federation denies being the source of the poison, suggesting it could have been another country, and has demanded that Britain share samples collected by investigators.
Moscow is also considering its response to the United States after Donald Trump's administration imposed sanctions on Russians allegedly involved in interfering with the 2016 USA elections and cyber-attacks.
The source of the nerve agent used - which Britain says is Soviet-made Novichok - is unclear.
Russian Federation has denied the accusations and has accused Britain of fabricating the story. The 67-year-old had been one of Russia's most powerful figures in the years after the collapse of the Soviet Union.
Defence secretary Gavin Williamson sparked particular outrage in Moscow with his blunt comment on Thursday that "Russia should go away, it should shut up".
Vil Mirzayanov, who now lives in New Jersey, is quoted in the Novaya Gazeta newspaper as saying that he revealed the existence of Novichok because he thought it was necessary to deprive Russian Federation of its "deadly secret".
Writing in the Guardian, Mr Corbyn, whose response to the attack has led to criticism from some on his backbenches, said "the evidence points towards Russia" being responsible - but the possibility of gangsters being behind the attack rather than the Kremlin could not be excluded.