The Prime Minister said investigators had established that the “military grade” nerve agent used against Sergei Skripal and his daughter Yulia is one produced by Russia.
Russia's ambassador has been given until the end of the day on Tuesday to explain Moscow’s involvement after being summoned by the Foreign Secretary this afternoon.
The UK's National Security Council will meet again on Wednesday to discuss its response to what Mrs May called an “indiscriminate and reckless act against the United Kingdom”.
Nicola Sturgeon called for "cool heads" and a "firm response" to the attack. "Russia simply cannot be allowed to launch attacks on our streets with impunity," she posted on Twitter.
Jeremy Corbyn called on the Russian government to explain its role, but was attacked by MPs including some from his own party after using the Prime Minister's statement to criticize the Tories over donations from sources with links to Russia.
Talks have already been held with the UK's allies at a senior official level to inform them of the findings by investigators in Salisbury, and to coordinate a response.
Updating the House of Commons, the Prime Minister said: “This morning I chaired a meeting of the National Security Council in which we considered the information so far available.
”As is normal, the council was updated on the assessment and intelligence picture, as well as the state of the investigation.
“It is now clear that Mr Skripal and his daughter were poisoned with a military-grade nerve agent of a type developed by Russia.”
Mrs May said the nerve agent, known as Novichok, has previously been produced by Russia, adding that Moscow had a “record of conducting state-sponsored assassinations” and “views some defectors as legitimate targets for assassinations”.
She said the government “has concluded that it is highly likely that Russia was responsible for the act against Sergei and Yulia Skripal.”
Mrs May told MPs: “There are therefore only two plausible explanations for what happened in Salisbury on 4 March: either this was a direct act by the Russian State against our country, or the Russian government lost control of this potentially catastrophically damaging nerve agent and allowed it to get into the hands of others.
“This afternoon the Foreign Secretary has summoned the Russian Ambassador to the Foreign and Commonwealth Office and asked him to explain which of these two possibilities it is – and therefore to account for how this Russian-produced nerve agent could have been deployed in Salisbury against Mr Skripal and his daughter.
“My Rt Hon Friend has stated to the Ambassador that the Russian Federation must immediately provide full and complete disclosure of the Novichok programme to the Organisation for the Prohibition of Chemical Weapons. And he has requested the Russian Government’s response by the end of tomorrow.”
Highlighting Russia’s annexation of Crimea, its involvement in conflict in Ukraine, and the killing of the former Russian agent Alexander Litvinenko in 2006, the Prime Minister added: “We have led the way in securing tough sanctions against the Russian economy, and we have at all stages worked closely with our allies and we will continue to do so.
“We must now stand ready to take much more extensive measures. On Wednesday we will consider in detail the response from the Russian State.
"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, and I will come back to this House and set out the full range of measures that we will take in response. We will not tolerate such a brazen attempt to murder innocent civilians on our soil.”