The UK Government said it "stands in full support" with the Czech Republic after authorities published photos of two foreign citizens who visited the country in 2014 and asked the public for any information about them.
The two were using Russian passports and were identified as Alexander Petrov, 41, and Ruslan Boshirov, 43.
It came as the Czech Republic said it was expelling 18 Russian diplomats who it had identified as spies in a case related to a huge ammunition depot explosion in the town of Vrbetice in 2014.
Petrov and Boshirov are wanted by police in the UK after the Crown Prosecution Service authorised charges against them in connection with the attempted killing of Sergei Skripal in Salisbury on March 4, 2018.
Speaking about the latest developments in the Czech Republic, foreign secretary Dominic Raab said: "The UK stands in full support of our Czech allies, who have exposed the lengths that the Russian intelligence services will go to in their attempts to conduct dangerous and malign operations in Europe.
"We are as determined and committed as ever to bring those responsible for the attack in Salisbury to justice, and commend the actions of the Czech authorities to do the same.
"Russia must desist from these actions, which violate the most basic international norms."
Czech police said the two men had visited the country between October 11 and 16, 2014, and that they also visited the capital of Prague and another north-eastern Czech region.
They said the suspects were also using passports issued by Moldova for Nicolai Popa and a passport issued by Tajikistan for Ruslan Tabarov.
An explosion on October 16, 2014 in a depot in the town of Vrbetice where 50 metric tons of ammunition was stored claimed two victims.
Another explosion of 13 tons of ammunition occurred in the depot on December 3 of that same year.
Mr Skripal, a former Russian spy turned double agent for MI6, and his 33-year-old daughter Yulia, survived the Novichok attack in Salisbury, but the incident later claimed the life of Dawn Sturgess after she came into contact with a perfume bottle believed to have been used in the attack before being discarded.
The suspects were seen on CCTV footage in Salisbury the day before the attack.
Moscow has repeatedly denied any involvement, with president Vladimir Putin claiming the two suspects were civilians.
The Russian ambassador to the UK has meanwhile said he has not seen foreign secretary Dominic Raab for more than a year amid rising tensions.
It comes after Mr Raab said the UK and US were determined to stand together against what he described as Russia's "malign behaviour" following a major cyber attack on the West.
Andrey Kelin was summoned to the Foreign Office to be told the UK will continue to work with allies "to call out and counter malign operations" by Moscow's spies.
Speaking to the BBC's Andrew Marr Show, Mr Kelin said: "If Dominic Raab is really seeing how Russia interferes or demolish democracy, I am ready to discuss it with him.
"But I haven't seen Secretary Raab for more than a year."