Britain has said the two suspects were Russian military intelligence officers nearly certainly acting on orders from high up in the Russian state.
"Of course we have checked out who these people are", Mr. Putin said at a forum in Vladivostok in response to a question from a reporter. "There is nothing criminal here".
Putin's declaration came seven days after British authorities announced that they had charged two Russian men, identified as Aleksandr Petrov and Ruslan Boshirov, with carrying out the poisioning on March 4. He was sentenced to prison in Russian Federation before being released in a spy swap in 2010.
He said that there was "nothing criminal" about the two men and that he hoped they would come forward and tell their own story, adding: "That would be better for everybody".
Putin said they were civilians who did not work for the military.
'I hope they will turn up themselves and tell everything.
"When one country's prime minister accuses the leaders of another country of preparing a terrorist attack, from this point we can not proceed anywhere", he added.
Ms Sturgess died in hospital in July, just over a week after the pair fell ill.
It has further damaged already severely strained relations between Russian Federation and the West and has been a cause for solidarity at a time when Western officials accuse Moscow of seeking to cause rifts in relations between Western countries.
In a statement that deepened the diplomatic crisis between the two countries, the Prime Minister said: 'The GRU is a highly disciplined organisation with a well-established chain of command.
They did a reconnaissance mission to Salisbury the following day before returning with poison concealed in a fake Nina Ricci perfume bottle.
Detectives believe the front door of Mr Skripal's Salisbury home was contaminated with Novichok.
The Skripals spent weeks in hospital in a critical condition after the poisoning.
Putin urged the two men to speak to journalists.