The agreement came after the Prime Minister set out a detailed account of the evidence which led the Government to point the finger of blame at the Kremlin during an EU summit in Brussels.
Reports suggested that as many as five EU countries - France, Poland and the three Baltic states - could now follow Britain’s lead by expelling suspected Russian spies.
European Council president Donald Tusk said: “European Council agrees with UK government that highly likely Russia is responsible for Salisbury attack and that there is no other plausible explanation.”
Earlier on Thursday, it was announced that the police officer exposed to the Novichok nerve agent had been discharged from hospital.
In a statement Detective Sergeant Nick Bailey said he had been “overwhelmed” by the messages of support, but acknowledged: “Normal life for me will probably never be the same.”
The EU statement came as a welcome boost to Mrs May in her increasingly bitter stand-off with Moscow over the attack on former double agent Sergei Skripal and his daughter, Yulia.
On Monday foreign ministers of the 28-nation bloc had issued a statement voicing “unqualified solidarity” with the UK, but stopping short of blaming the Russians.
In her address to the other 27 EU leaders over dinner, the Prime Minister set out the four pillars of evidence which the UK believe put Russia in the frame:
- The positive identification by experts at Porton Down of the specific chemical used as a type of Novichok nerve agent;
- The knowledge that Russia has produced this agent within the last 10 years and remains capable of doing so;
- Russia’s record of conducting state-sponsored assassinations; and
- Britain’s assessment that Russia views defectors as suitable targets for assassination.
German chancellor Angela Merkel was one of several leaders to express solidarity with the UK after meeting Mrs May and France’s president Emmanuel Macron on the margins of the summit to discuss the incident.
Lithuania’s president Dalia Grybauskaite disclosed the she was considering following Britain’s example by expelling Russian spies from her country.
Resistance to a firmer line with Moscow apparently came from Greece, whose prime minister Alexis Tsipras said: “We have to express solidarity to the British people for the Salisbury case, but we also need to be responsible on that issue.”
Meanwhile a Court of Protection judge has given doctors permission to take blood from the Skripals - who remain in a critical condition in hospital - and to provide samples to chemical weapons experts.
Mr Justice Williams said he had been asked to make decisions because Mr and Ms Skripal were unconscious and therefore unable to give their consent to blood samples being taken or tested.