"We have full confidence in the British assessment that the two suspects were officers from the Russian military intelligence service, also known as the GRU, and that this operation was nearly certainly approved at a senior government level", the statement said, adding that the countries urged Russia to provide "full disclosure of its Novichok program".
Police say the men travelled on Russian passports bearing the names Petrov and Boshirov, but that these are nearly certainly aliases.
Speaking before Scotland Yard's statement, the Kremlin spokesman Dmitry Peskov said Moscow had repeatedly offered to cooperate with Britain in the Skripal investigation but had been met with "either refusal or silence".
A European arrest warrant has been issued for the two Russians, who were named as Alexander Petrov and Ruslan Boshirov, the prosecutors said.
Sue Hemming of the Crown Prosecution Service said the United Kingdom wouldn't ask Moscow to extradite the men because Russian law forbids extradition of the country's citizens.
"[This] means that if either man travels to a country where an EAW is valid, they will be arrested and face extradition on these charges for which there is no statute of limitations".
US Ambassador Nikki Haley said everyone should be "chilled to the bone" with the findings.
Former Russian spy Sergei Skripal's niece on Thursday begged her uncle, who was poisoned in Britain, to call his 90-year-old mother to prove he was alive. Both Skripal, a GRU officer who turned double agent for Britain, and his daughter were hospitalized for weeks in critical condition. Her boyfriend Charlie Rowley also became seriously ill during that incident, and police officer Nicholas Bailey was hospitalised by exposure to the Skripals at the time of the first incident.
Investigators determined they were sickened by a Soviet-designed nerve agent called Novichok. Mr. Basu said the passports were genuine but the men were probably using aliases, and appealed the public "to come forward and tell us who they are".
In a statement from the Metropolitan Police Wednesday morning, counter-terror boss Assistant Commissioner Neil Basu said 250 counter-terror officers had been involved in the investigation, and that an Interpol red notice would be circulated for the men.
Police also produced photographs of a Nina Ricci perfume box, and a false perfume bottle inside with an extended nozzle, which they said had been brought over from Russian Federation to smuggle the nerve agent into the UK.
Her partner, Charlie Rowley, 48, was also treated in the same Salisbury hospital and later released. He was hospitalised and his girlfriend Dawn Sturgess, 44, died after being exposed to the contents.
The Organization for the Prohibition of Chemical Weapons confirmed Tuesday that Mr. Rowley and Ms. Sturgess were also exposed to Novichok.
Police are still trying to determine where the bottle was between the Skripal poisoning in March and its discovery by Rowley on June 27.
The CPS said the pair faced charges of conspiracy to murder Skripal, and the attempted murder of him, his daughter and Nick Bailey, a policeman injured in the attack. Sturgess later died from exposure to the agent.
Basu would not comment on whether the Skripals had faced threats before the attack or where they were now located.
There is also likely to be less visible activity including covert work by British intelligence to try to disrupt the activities of the Russian military intelligence agency, including in cyberspace.
The Kremlin rejected the claims that Mr Putin was responsible and said that it was not going to investigate the suspects.