The US President made the pledge in a telephone call with the Prime Minister just a day after the White House refused to echo Mrs May's claim that the Kremlin was "highly likely" to have been responsible for the attack.
Former Russian spy Sergei Skripal, and his daughter Yulia remain in hospital after being found unconscious on a shopping centre bench in Salisbury, Wiltshire, nine days ago. Detective Sergeant Nick Bailey, who was the first to respond to the incident, is also still receiving treatment.
In the Commons yesterday, Mrs May gave Russia's ambassador to the UK 24 hours to explain to the Foreign Office what had happened.
She said: “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."
But while White House spokeswoman Sarah Huckabee Sanders told journalists the attack was "reckless, indiscriminate and irresponsible", she refused to point the finger at Russia.
In a dramatic development, US Secretary of State Rex Tillerson - who had blamed Russia for the attack - was sacked from his post by President Trump.
Speaking after the phone call between Mrs May and President Trump, a Downing Street spokesperson said: "The Prime Minister set out the conclusion reached by the UK government that it was highly likely that Russia was responsible for the attack against Sergei and Yulia Skripal.
"President Trump said the US was with the UK all the way, agreeing that the Russian government must provide unambiguous answers as to how this nerve agent came to be used."
Meanwhile, German Chancellor Angela Merkel has told Mrs May she stands "in full solidarity" with the UK.
The Downing Street spokesperson said: "They discussed the pattern of aggressive Russian behaviour and agreed it would be important to act in unison with allies to counter it.
"Chancellor Merkel condemned the attack and said she stood in full solidarity with the UK. They agreed that the international community should co-ordinate closely as the investigation developed and in the wake of Russia’s response.”
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