The Prime Minister said Russia had the capability, motive and intent to carry out such an attack, adding that there can be “no other conclusion”.
Mrs May’s comments followed strong words from Boris Johnson, who accused Russia of trying to conceal “the needle of truth in a haystack of lies” over the case - after Mr Putin dismissed the idea of Russian responsibility as “nonsense”.
Arriving for a meeting with EU counterparts in Brussels, the Foreign Secretary said Moscow’s denials over the incident were “increasingly absurd” as he accused the Kremlin of changing its story regarding the Novichok nerve agent Britain says was used in the attack.
The gathering of the EU Foreign Affairs Council declared its “unqualified solidarity” for the UK over the incident.
Experts from the Organisation for the Prohibition of Chemical Weapons (OPCW) arrived in the UK yesterday to take samples of the nerve agent used in the case.
Mr Johnson said: “At one time they (Russia) say that they never made Novichok, and at another time they say they did make Novichok, but all the stocks have been destroyed ... but some of them have mysteriously escaped to Sweden, or the Czech Republic, or Slovakia, or the United States, or even ... the United Kingdom.
“I think what people can see is that this is a classic Russian strategy of trying to conceal the needle of truth in a haystack of lies and obfuscation.”
Mrs May said: “I’m clear that what we have seen shows that there is no other conclusion but that the Russian state is culpable for what happened on the streets of Salisbury.”
Following reports around the possible exhumation of bodies of other Russians who died in suspicious circumstances, she added that it is a “matter for the police”.
Mr Putin dismissed claims of Russia being behind the poisoning as “nonsense” as he was re-elected president.
Sergei Skripal and his daughter Yulia would have died instantly if they had been attacked with a nerve agent, the leader said as he celebrated the start of another six-year term.