Prime Minister May said last week that the men were agents from Russia's GRU military intelligence and that the Kremlin had "almost certainly" authorized the attempted murder and the use of the nerve agent Novichok on British soil.
London's reaction to a recent interview of Russia's RT channel with two men suspected of poisoning Sergei Skripal and his daughter Yulia is absurd, Russian Presidential Spokesman Dmitry Peskov said on Friday.
"Our friends had been suggesting for a long time that we visit this wonderful town", the man identified as Petrov said. They said they had fallen victim to a "fantastical coincidence". Putin said Russian officials "know who these people are" and called on the two men to talk to the media and "tell about themselves".
Britain said the attack was nearly surely approved at a top level of the Russian government.
They said there was enough evidence to prosecute them of conspiring to murder former Russian Federation spy, Sergei Skripal, and his daughter with a military-grade nerve agent in Salisbury, England, in March, but the government said seeking their extradition from Russian Federation was futile.
Ms Sturgess died in hospital in July, just over a week after the pair fell ill.
Britain identified the Russian suspects last week and released security-camera photos of them in Salisbury on March 3 and 4.
Speaking with RT editor-in-chief Margarita Simonyan, the two confirmed they were the men being shown in CCTV footage by British authorities. The weather was better on the 4th, Petrov said, so the two returned to see Stonehenge and the cathedral.
They again were recorded in the center of town an hour later and were at the station by 1:50 p.m., two hours after arriving.
Asked about his biggest professional mistake at an event in Washington DC last night he said: "When I became foreign secretary I thought there was no objective reason why we should be quite so hostile to Russian Federation".
Skripal and his daughter were found unconscious on a shopping mall bench on March 4 in Salisbury, a city about 90 miles west of London.
Asked about apparent inconsistencies in the two men's story, 44-year-old Muscovite Ivan Raspopov joked: "You know, Russian tourists often become rather odd in the West". "You spend time together, you live together, you walk together. what do you have in common that you spend so much time together?'"
Boshirov replied: "Let's not pry into our private lives". "We pick up the most necessary, come here and decide how to deliver the new products from this market here".
They said that they had previously travelled to Europe for business and pleasure.
"Russia's position has remained unchanged and clear - we consider it unacceptable to link the Russian leadership or the Russian state to what happened in Salisbury", Peskov said. "What is our fault?"
"Do you know where Skripal's house is?" asked Boshirov.
Forget about London, travel straight to Salisbury.
Ruslan Boshirov and Alexander Petrov spoke with the government TV station RT in their first public appearance since they were named as suspects. "But very unusual to come all this way for just two days while carrying Novichok in their luggage", Tweeted John Glen, the Member of Parliament for Salisbury.
Lawless reported from London. Associated Press writer Nataliya Vasilyeva in Moscow contributed.