His comments will further increase tensions between Moscow and London, which are at their lowest levels since the Cold War.
Senior politicians have exchanged furious broadsides since the horrific nerve attack in Salisbury, Wiltshire earlier this month.
Mr Peskov told state news agency RIA: “We are stating that this is quite unprecedented – international affairs bordering, maybe, on banditry.
“What stands behind this? Is it Britain’s internal problems, or the problems of Britain’s cooperation with its allies or something else?
“It looks like this is not our business.”
Moscow has repeatedly denied responsibility for the March 4 attack on 66-year-old Mr Skripal and his daughter, Yulia, 33.
The incident, which triggered a major diplomatic row, was the first known offensive use of a nerve toxin in Europe since World War 2.
The UK expelled 23 Russian diplomats as a result and Moscow retaliated by ordering out the same number of Britons.
Earlier this week, Mr Skripal’s friend Vladimir Timoshkov revealed the ex-double agent had written to Mr Putin asking to be pardoned.
Mr Timoshkov said Mr Skripal, who came to Britain in 2010 as part of a spy swap, wanted to return to Russia to visit his family.
The 66-year-old was accused of working for MI6 over several years, in particular disclosing the names of Russian agents working in Europe.
He was sentenced to 13 years in a high-security prison in August 2006.
However, he was freed in the 2010 deal which saw 10 Russian sleeper agents expelled from the United States.
According to Mr Timoshkov, his friend, who he had known since school, did not see himself as a traitor as he had sworn an oath to the Soviet Union.
He said: “Many people shunned him. His classmates felt he had betrayed the Motherland.
“In 2012 he called me. We spoke for about half an hour. He called me from London. He denied he was a traitor.
“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.”