U.S. President Donald Trump said it looked like the Russians were behind it.
"We do hold Russian Federation culpable for this brazen, brazen act and despicable act", Prime Minister Theresa May said during a visit to the site of the attack in Wiltshire. "Something that should never, ever happen, and we're taking it very seriously".
Russian Federation has repeatedly denied any involvement in the attack, the first offensive use of a nerve agent in Europe since World War II.
"Maybe he lacks education", Mr Lavrov said.
"We share the United Kingdom assessment that there is no plausible alternative explanation, and note that Russia's failure to address the legitimate request by the United Kingdom government further underlines its responsibility", it adds.
In the biggest expulsion of Russian diplomats from London since the Cold War, Prime Minister Theresa May on Wednesday gave 23 Russians who she said were spies working under diplomatic cover a week to leave London.
Russian foreign minister Sergey Lavrov had earlier said Moscow had "stopped paying attention" to British claims about the poisoning.
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The UK Government has said it is "highly likely" that Russian Federation was behind the attack but until now has not directly suggested Mr Putin was personally responsible for ordering the poisoning, which used the "military grade" nerve agent Novichok.
Lavrov said British accusations of Moscow's involvement are meant to distract public attention from the U.K's troubled exit from the European Union.
Dmitry Peskov, the Kremlin spokesman, said Russian Federation was "worried by this situation" and would work to express its position on the worldwide stage.
Britain also said it would invest 48 million pounds ($67 million) in a new chemical warfare defence centre at its Porton Down military research laboratory, where scientists identified the nerve agent used against Skripal.
"We call on Russian Federation to live up to its responsibilities as a member of the UN Security Council to uphold worldwide peace and security", they said.
Both Skripal and his daughter are in critical condition and doctors aren't sure if they'll survive.