Putin, speaking at an economic forum in Vladivostok, said of the Salisbury suspects: "We know who they are, we have found them".
Britain last week named two men as key suspects in the nerve-agent poisoning of Sergei Skripal and his daughter.
"We know who they are, we have found them", Mr Putin said in the far eastern city of Vladivostok.
"I hope they will turn up themselves and tell about themselves", he said. This would be best for everyone.
"There is nothing special there, nothing criminal, I assure you".
"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. "Hours after their final visit to Salisbury, they took a late-night flight back to Moscow on March 4 - the same day the Skripals were sickened".
Mr Skripal and Yulia were poisoned in Salisbury in the United Kingdom in March.
The CPS is not applying to Russian Federation for the extradition of the two men, as Russian Federation does not extradite its own nationals.
The Skripals survived the poisoning but a local man, Charlie Rowley, picked up a fake perfume bottle containing Novichok weeks later. Sturgess died in hospital on July 8. Investigators said the banned Soviet-era nerve agent novichok was found on the front door to their home. A police officer who found them was also hospitalized.
Citing the GRU's reputation for strict discipline and hierarchy, May said of the attack on the Skripals, "It was nearly certainly also approved outside the GRU, at a senior level of the Russian state". His partner, Ms Sturgess, applied some of the contents to her wrists and became unwell.
Putin and Russian Federation have vehemently denied having anything to do with the poisoning cases.
Britain and dozens of other countries kicked out scores of Russian diplomats over the poisoning of the Skripals, and Moscow responded tit-for-tat with an identical number of expulsions. UK Prime Minister Theresa May has also said Britain will push for the European Union to agree new sanctions.
Detectives believe it is likely the two Salisbury suspects, thought to be aged around 40, travelled under aliases and that Mr Petrov and Mr Boshirov are not their real names.
The head of center-left opposition party Fair Russia says Moscow should sever diplomatic relations with London over recent unfounded accusations regarding the Skripal case - as he believes there is no scope to settle the dispute.