British Foreign Secretary Boris Johnson said Britain's quarrel was not with the Russian people but with the Kremlin.
The sanctions affect 13 Russian nationals and three entities aligned with the Internet Research Agency (IRA), a group that in essence serves as Russia's propaganda arm and is believed by US intelligence to have been behind divisive online ads released during the election.
"Our quarrel is with Putin's Kremlin, and with his decision - and we think it overwhelmingly likely that it was his decision - to direct the use of a nerve agent on the streets of the United Kingdom".
Sergei Skripal moved to Salisbury after being jailed for passing Russian state secrets to British intelligence while working for the Russian government in the 1990s.
Russian Federation has refused Britain's demands to explain how Novichok, a nerve agent developed by the Soviet military, was used to strike down Sergei Skripal, 66, and his daughter Yulia, 33, in the southern English city of Salisbury.
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Tensions with Moscow are growing before Russia's presidential election Sunday, after a nerve agent attack in Britain on a Russian ex-spy.
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.
Russian Foreign Minister Sergey Lavrov told a forum promoting investment in his country that many other nations had "a very nervous reaction" to Russia's rise from post-Soviet chaos into a leading world power in the past two decades.
The Kremlin's Peskov called the allegation that Putin was involved "a shocking and unforgivable breach of the diplomatic rules of decent behaviour", TASS news agency reported.
May's office said in a statement that the two leaders spoke about the attempted murder of former spy Sergei Skripal, 66, and his 33-year-old daughter, Yulia.
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Russian Federation denies being the source of the nerve agent used and has demanded Britain share samples collected by investigators.
Lavrov said Russian Federation will "of course" expel British diplomats and that he hopes the Skripals recover soon so light can be shed on what happened.
The Kremlin has repeatedly denied any involvement in the killing.
The United States, France and Germany also condemned Russian Federation over the attack.
Britain says the Russian state is behind the poisoning of ex-spy Sergei Skripal and his daughter in the English city of Salisbury.
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"It threatens the security of us all", they added, without spelling out any possible further reprisals.