Mr Peskov said Mr Skripal was of “zero importance” to Russia, as the Kremlin would only release a spy if they were of no threat.
The former double agent was handed over to Britain in 2010 as part of a spy swap in which Russia released four British spies, including Skripal, in exchange for 10 Russian agents.
The former army colonel was sentenced to 13 years in jail for passing the identities of Moscow agents working undercover in Europe to MI6 in 2006 but arrived in the UK four years later as part of a high-profile swap.
Mr Peskov said: “We’re not speaking about an attempt to murder a Russian spy in Great Britain; we’re speaking about an attempt to murder a British spy Great Britain.
“He was handed into Britain as a result of an exchange, so why should Russia hand in a man that is of any importance or value? It’s unimaginable.
“If he’s handed in, then Russia quits with him.
“He’s of zero value and zero importance.”
Mr Peskov accused the UK authorities of being too hasty in blaming Russia without carrying out a full investigation.
Mr Peskov, speaking with Russia’s international state news website RT: “The first accusations came from politicians just a couple of hours after the accident.
“We heard the first accusation that it was highly likely that Russia was responsible for that attempted murder.
“Now we see words of experts of organisations for OPCW (Organisation for the Prohibition of Chemical Weapons) that the preliminary examining of this agent will take three weeks.
“Is it contradictory? Yes, it is.”
Mr Peskov cited the words of Mr Putin, adding “we’re not crazy to think of something of that kind before the presidential elections and such as important global event such as the football championship”.
The comments come as British Prime Minister Theresa May prepares to put pressure on EU leaders to join the UK in expelling Russian diplomats and warning them “we are all at risk” of a brazen Mr Putin at dinner with member state leaders tonight.
The EU, and separately France and Germany, has offered its “solidarity” with the UK after the attack on the Skripals.
Earlier this week, the UK expelled 23 Russian diplomats, leading to the Russian President to retaliate by expelling the same number of British officials based in Moscow.