Former Russian spy Sergei Skripal, 66 and his daughter Yulia, 33 were found collapsed after being poisoned last Sunday. Skripal and Yulia remain in a serious condition along with a police officer who came in contact with the same substance.
In a statement before the House of Commons, May revealed that the UK's security forces have now confirmed that the poison used in the attack on Skripal was a "military-grade" nerve agent of the type developed by Russia.
"It is now clear that Skripal and his daughter were poisoned with a military-grade nerve agent of a type developed by Russia. This is part of a group of nerve agents known as Novichok'," May said in her statement.
"Based on the positive identification of this chemical agent by the world-leading experts, our knowledge that Russia has previously produced this agent and would still be capable of doing so," she said.
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Russia's record of conducting "state-sponsored assassinations and our assessment that Russia views some defectors as legitimate targets for assassinations; the government has concluded that it is highly likely that Russia was responsible for the act against Sergei and Yulia Skripal, she said.
The British prime minister said Russia's response would be assessed in detail on Wednesday to determine further action.
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," she said
"This attempted murder using a weapons-grade nerve agent in a British town was not just a crime against the Skripals. It was an indiscriminate and reckless act against the United Kingdom, putting the lives of innocent civilians at risk," May said.
In her Parliament statement, May made a specific reference to the use of radiological substances in the "barbaric assault" on Alexander Litvenenko another Russian spy murdered 11 years ago in London.
Following Litvinenko's death, the UK had expelled Russian diplomats, suspended security cooperation, broke off bilateral plans on visas, froze the assets of the suspects and put them on international extradition lists. May told Parliament that those measures remain in place.
We must now stand ready to take much more extensive measures, she added.
The country's "illegal annexation" of Crimea was the first time since the Second World War that one sovereign nation has forcibly taken territory from another in Europe, she said.
However, her statement reiterated that while the poisoning of the Skripals had caused considerable concern in the local community of Salisbury, the risk to public health remains low.
"The statement was part of an information and political campaign based on provocation," said Russian foreign ministry spokeswoman Maria Zakharova.
Colonel Skripal was convicted of treason in 2006 and jailed for 13 years for selling secrets to MI6, which had recruited him in the 1990s. The senior intelligence officer with Russian military intelligence GRU, was pardoned in a spy swap in 2010 and settled in Salisbury, Wiltshire.
The attack on Skripal is being compared to former KGB agent Litvenenko's murder who ingested the rare and highly radioactive polonium 210 in London 11 years ago.