Theresa May is pressing for a united statement from the European Union condemning Russia for the nerve agent attack in Salisbury.
Foreign ministers of the 28-nation bloc issued a statement on Monday voicing "unqualified solidarity" with the UK, but stopping short of pointing the finger of blame at Moscow for the March 4 attack on ex-spy Sergei Skripal and his daughter Yulia.
Arriving in Brussels for a summit of the European Council, Mrs May said she would brief fellow leaders on the "brazen and reckless" use of chemical weapons on European soil and leave no doubt that she sees it as part of a pattern of Russian aggression which requires a united response.
Britain has been pressing EU allies behind the scenes to follow its expulsion of 23 "undeclared intelligence officers" from Russia's embassy in London by sending home Moscow's spies in their own countries.
Mrs May is set to address the other 27 EU leaders over dinner on her belief that Europe faces a challenge from Russia that will last many years and represents a threat to the continent's democracy.
Wearing a white ribbon in commemoration of terror attacks in Westminster and Brussels, the Prime Minister said: "Russia staged a brazen and reckless attack against the United Kingdom when it attempted the murder of two people in the streets of Salisbury.
"I will be raising this issue with my counterparts today because it is clear that the Russian threat doesn't respect borders and indeed the incident in Salisbury was part of a pattern of Russian aggression against Europe and its near neighbours from the western Balkans to the Near East."
Meanwhile, in London, Russia's ambassador Alexander Yakovenko condemned Foreign Secretary Boris Johnson's comparison between Mr Putin hosting this summer's World Cup with Hitler's 1936 Olympics as an "insult" to the Russian people.
Mr Yakovenko demanded evidence for Britain's allegation that Russia was behind the Salisbury attack, saying official statements on the poisoning had been "wild" and the UK had "built its official position on pure assumptions".
At a press conference at his London residence, not far from Kensington Palace, he said: "We demand full transparency of the investigation and full cooperation with Russia and with the OPCW (Organisation for the Prohibition of Chemical Weapons)."
Mr Johnson had escalated the war of words with Moscow by suggesting that Vladimir Putin is hoping for a propaganda boost from this summer's World Cup similar to that which Hitler sought in the 1936 Berlin Olympics.
Mr Yakovenko condemned the comments, saying: "Nobody has the right to insult the Russian people, who defeated Nazism."
He said the comparison "goes beyond common sense".
He added that the response of the Government and various statements since the incident had created "serious problems" in the Russia-UK relationship.
He said: "What really worries me is that the way this campaign is being presented is very anti-Russian. It really creates serious problems for the UK itself.
"Because after two weeks of this kind of really wild statements, how are you going to talk to the Russians?
"Because as I said that was really very insulting to the Russian people. It's not about government, we're talking about people."