Putin broke his silence on Wednesday a week after British authorities named the men suspected of trying to murder Sergei Skripal and his daughter Yulia in Salisbury, Wiltshire, in March.
Speaking at an economic forum with Japan's Shinzo Abe and China's Xi Jinping in the far eastern city of Vladivostok, Putin urged the men to address the media and said there was "nothing criminal".
He added with a smirk, "I hope they will soon appear and tell their own story".
Britain last week charged two alleged agents of Russia's military intelligence agency in absentia with the nerve agent poisoning of former Russian spy Sergei Skripal and his daughter Yulia in the English city of Salisbury.
Russian Federation has repeatedly contested the allegations and on Wednesday Putin escalated the war of words by denying the men were members of military intelligence.
A handout picture taken on Fisherton Road in Salisbury shows Petrov and Boshirov on March 4, 2018, in a photo released by the British Metropolitan Police Service.
'There is nothing special there, nothing criminal, I assure you.
Police are linking the attack to a separate Novichok poisoning on 30 June, when Dawn Sturgess and Charlie Rowley became unwell at a house in Amesbury, about eight miles away.
"I would like to call on them so that they can hear us today", he said.
Kremlin spokesman Dmitry Peskov said the president has not communicated with the men themselves since they were accused of poisoning the Skripals.
London and its allies expelled dozens of Russian diplomats after the poisoning, prompting a tit-for-tat response from Moscow and plunging relations to a new low. Russian Federation kicked out a similar number of those countries' envoys. One of them, a 44-year-old woman, later died.
UK Prime Minister Theresa May has previously said the attack was "almost certainly" approved at a "senior level" of the Russian state, while Security Minister Ben Wallace said Putin bore ultimate responsibility as head of the government in Moscow.
An Interpol Red Notice and European arrest warrant have been issued, though the Russian Constitution forbids them from being extradited.