"They are just ordinary civilians", Putin told a session at an economic forum in Vladivostok broadcast on state TV.
At the time, British Prime Minister said intelligence indicated the men were officers in the GRU, and the attack would have been approved "at a senior level of the Russian state".
Russian Federation has hotly contested the allegations that it is responsible for the attack, and on Wednesday Mr Putin escalated the war of words by denying the men were members of military intelligence, and that his officials "know who these people are".
We have checked what kind of people they are. "It will be better for everyone", he said.
He added, "There is nothing special or criminal about it, I can assure you". "They should go to some media outlet".
United Kingdom authorities have named the men as Alexander Petrov and Ruslan Boshirov, thought to be officers of Russia's military intelligence service, the GRU.
Putin's remarks appeared to be a denial that the men worked for Russia's military intelligence service, the Main Directorate, commonly called the GRU.
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Mr Wallace later said requests for Russian Federation to account for what happened in Salisbury had been met with "obfuscation and lies", saying their response merely "reinforces their guilt".
The statement by Putin marked an abrupt shift from Russia's earlier position on the poisoning case that has damaged relations between Moscow and the West.
The Kremlin said on Wednesday that Putin had not spoken to the two accused men and refused to say how and by whom they had been found.
Scotland Yard released photos of the men last week, saying they're wanted in connection to a poisoning attack on a former KGB agent.
Calling the poisoning a "sickening and despicable" attack, Javid said it was "unequivocally, crystal-clear this was the act of the Russian state - two Russian nationals sent to Britain with the sole goal of carrying out a reckless assassination attempt".
Alexander Petrov and Ruslan Boshirov, who were formally accused of attempting to murder former Russian intelligence officer Sergei Skripal and his daughter Yulia in Salisbury, are seen in an image handed out by the Metropolitan Police in London, Britain September 5, 2018. The affair worsened Russian relations with the West, already under strain over Ukraine, Syria and other issues.