The PM said the government concluded it was “highly likely” Russia was responsible for the Salisbury attack.
Russia’s ambassador has been asked to explain whether it was “direct action” by the state or due to it “losing control” of its nerve agent stock.
The Russian Foreign Ministry labelled Mrs May’s remarks a “fairy tale”.
The chemical used in the attack, the PM said, has been identified as being part of a group of nerve agents known as Novichok.
Mrs May said Foreign Secretary Boris Johnson had told the ambassador Moscow must provide “full and complete disclosure” of the Novichok programme to the Organisation for the Prohibition of Chemical Weapons by the end of Tuesday.
“Should there be no credible response, we will conclude that this action amounts to an unlawful use of force by the Russian state against the United Kingdom.”
In that event, she said she would return to the Commons on Wednesday “and set out the full range of measures that we will take in response”.
Sixty-six-year-old retired military intelligence officer Mr Skripal and his daughter, 33, were found slumped on a bench in Salisbury city centre. They remain in a critical but stable condition.
Det Sgt Nick Bailey, who fell ill attending the pair, remains seriously ill in hospital but has been talking to his family.
Addressing the Commons following a meeting of the government’s National Security Council, Mrs May told MPs the positive identification of this chemical agent was made by experts at the UK’s Porton Down laboratory.
She said Russia has previously produced the agent and would still be capable of doing so.
The decision to point the finger at Moscow was also based on “Russia’s record of conducting state-sponsored assassinations and our assessment that Russia views some defectors as legitimate targets for assassinations”, the PM added.
Russian Foreign Ministry spokeswoman Maria Zakharova said Mrs May’s statement was “a circus show in the British parliament”.
“The conclusion is obvious – it’s another information and political campaign based on provocation,” she said.
Earlier, asked whether Russia was to blame, President Vladimir Putin told the BBC: “Get to the bottom of things there, then we’ll discuss this”.
Police activity continued on Monday afternoon, with officers – some wearing hazardous materials suits- removing a white van from the village of Winterslow, about six miles from Salisbury.
A Sainsbury’s car park in Salisbury was also sealed off by police.
Mr Skripal was convicted by the Russian government of passing secrets to MI6 in 2004, but given refuge in the UK in 2010 as part of a “spy swap”.
On Sunday, up to 500 Salisbury pub-goers and diners were told to wash their possessions as a precaution after trace amounts of the substance used to poison Sergei and Yulia Skripal were found on and around a table where they had eaten in Zizzi.
Traces were also found at the Mill pub in the city, which like Zizzi remains closed.
A Freelance Journalist, Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A contributory writer for Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
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