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.
British Prime Minister Theresa May squarely blamed Russia's military intelligence service on September 5 for carrying out the attack, adding that the upper echelons of the Russian state could also have been involved.
British authorities established that the Russian agents had carried out a reconnaissance trip to Salisbury prior to returning to the city and putting the novichok, carried in a bottle of counterfeit Nina Ricci perfume, on the front door of the Skripals' home.
Putin urged the men to speak to journalists.
Russian President Vladimir Putin gestures as delivers a speech Wednesday during a plenary session at the Eastern Economic Forum in Vladivostok, Russia.
There's nothing special and criminal about it, I assure you.
Putin added that the two men do not work for the military and that there is "nothing criminal" about them, calling them "civilians", the Associated press reported.
Kremlin spokesman Dmitry Peskov later told reporters that Putin never met the suspects in the poisoning and that Russian Federation did not investigate them but merely "checked the reports".
The attack in Salisbury prompted an global row, with more than 20 countries expelling Russian envoys in solidarity with the United Kingdom, including the USA, while Moscow expelled diplomats in response. They spent weeks in hospital before being discharged. One of them, a 44-year-old woman, later died.
"The GRU is a highly disciplined organization with a well-established chain of command, so this was not a rogue operation, it was nearly certainly also approved outside the GRU at a senior level of the Russian state", she said in a statement to the House of Commons last week.
Her spokesman, James Slack, rejected the claim the men were civilians, saying they were GRU officers "who used a devastatingly toxic illegal chemical weapon on the streets of our country".
The prime minister's official spokesman said the government had "repeatedly asked Russian Federation to account for what happened in Salisbury" but that Moscow "had replied with obfuscation and lies". "I can see nothing to suggest that has changed". "And with the new software they have, you can tell the person by the way they walk, or a ring they wear, or a watch they wear".
The pair flew back to Moscow from Heathrow later that night. Russian Federation kicked out a similar number of those countries' envoys. But a European arrest warrant has been obtained in case they travel to the EU, the BBC said.
"These two individuals travelled on a genuine Russian passport, making it harder to spot", Security Minister Ben Wallace has told the Commons.
The elder Skripal, who was a Russian intelligence agent who switched sides, as well as his daughter, survived the poisoning and now live in an undisclosed location.
His hint that the men could soon break their cover recalls memories of the assassination of former KGB agent Alexander Litvinenko on British soil, when killers Andrey Lugovoy and Dmitry Kovtun publicly refuted the allegations from Russian Federation.
Associated Press writer Jim Heintz in Moscow and Jill Lawless in London contributed.