The two men are also wanted over the attempted murder of an ex-Russian spy in the English city of Salisbury.
An alleged Russian plot to infiltrate a chemical weapons laboratory where samples of the poison Novichok were being tested has been foiled.
Two Russian men identifying themselves as the suspects in the poisoning of an ex-Soviet agent in the English countryside said they were just sightseeing.
Moscow has cast doubt over the relevance of the footage showing two Russian nationals visit the U.K., travel to Salisbury and leave during the attack.
The U.K. cannot seek an extradition from Russia, but a European arrest warrant has been issued.
Police are combing thousands of hours of closed-circuit TV footage.
The Russian government previously accused British intelligence officials of carrying out the Skripal poisoning as a way to stir up anti-Moscow sentiment.
The man and woman who fell ill in Amesbury were exposed to the same nerve agent that hospitalized a former Russian agent and his daughter.
The suspected poisoning incident occurred a few miles away from where former Russian spy Sergei Skripal and his daughter were attacked with a nerve agent.
The ex-Russian spy and his daughter were hit with an attack that used 50-100 grams of Novichok, the head of the OPCW has said.
Vladimir Uglev identified the poison that hospitalized former double agent Sergei Skripal as Novichok.
The man who may have invented the poison that took down Sergey Skripal has said he supports the British government's stance on Russia.
Meanwhile, Russia's foreign minister accused the U.K. of arm-twisting other countries to "demonize Russia."
U.N. Ambassador Nikki Haley slams Russia over alleged nerve attack.
Convicted Russian spy Sergei Skripal's "substance exposure" is drawing comparisons to the 2006 death of Russian intelligence agent Alexander Litvinenko's acute radiation poisoning.