Skripal, who came to Britain in 2010 as part of a spy swap, wrote to the Russian president denying he was “a traitor” and asked for “complete forgiveness”, according to comments made to the BBC by his friend Vladimir Timoshkov.
Both Skripal and his daughter Yulia remain in a critical condition after they were poisoned with the nerve agent Novichok in Salisbury on March 4.
The Russian embassy based in the UK wrote on social media on Saturday that there was “no letter” from Skripal to Putin.
Moscow has stepped up its campaign to discredit Theresa May’s assertion that it is “highly likely” Russia was responsible for the attack.
The Russian embassy in London reiterated its suggestion that the Porton Down defence laboratory was developing its own “military-grade poisons”.
The lab, located less than 10 miles from Salisbury, is where tests were carried out to identify the Novichok substance.
Porton Down chief executive Gary Aitkenhead told the BBC: “We have got the highest levels of controls, of security around the work that we do here.
“We would not be allowed to operate if we had lack of control that could result in anything leaving the four walls of our facility here.”
A Russian embassy spokesman said Aitkenhead’s comment “amounts to admitting that the secret facility is a place where new components of military-grade poisons are being researched and developed”.
Donald Tusk, the EU Council President, has said the 28 leaders agree it is “highly likely” the Russian state is responsible for the attack as there is “no other plausible explanation”.
EU leaders on Friday promised an “unprecedented” diplomatic response to the attack after backing May’s assertion that Moscow was responsible.
The bloc is recalling its ambassador to Russia for “consultations” on the Salisbury attack.
Russia has vehemently denied any responsibility for the incident.
Skripal, 66, was accused of working for MI6 over several years, in particular disclosing the names of several dozen Russian agents working in Europe.
He was sentenced to 13 years in a high-security prison in August 2006, before being freed in the 2010 deal which saw 10 Russian sleeper agents expelled from the United States.
According to his friend Timoshkov, who he had known since school, Skripal did not see himself as a traitor as he had sworn an oath to the Soviet Union.
“Many people shunned him. His classmates felt he had betrayed the Motherland,” he said.
“In 2012 he called me. We spoke for about half an hour. He called me from London. He denied he was a traitor... (he told me) he wrote to Vladimir Putin asking to be fully pardoned and to be allowed to visit Russia. His mother, brother and other relatives were (in Russia).”