"There's a need to finally turn this page -- linked to spies and assassination attempts," Putin told heads of global news agencies at an economic forum in Saint Petersburg.
"Global issues related to national interests in the economic and social spheres and global security are more important than games of security services," the Russian president said.
Putin added that Skripal was not a "Russian spy."
"It was not us who spied on you," Putin said. "It's your agent, not ours. That means you were spying on us."
Skripal is a former double agent, who sold secrets to Britain and moved there after a 2010 spy swap.
Last year Skripal and his daughter were poisoned with a military-grade nerve agent in the English city of Salisbury, the first use of chemical weapons in Europe since World War II.
London says the military grade nerve agent dubbed "Novichok" was produced in Russia and the attempted assassination was "almost certainly" approved by the Russian state.
Moscow has denied involvement.
Putin expressed hope that Moscow's ties with London will improve under a new prime minister in Britain, suggesting the new leader should think about British companies operating in Russia.
"I would very much want a person who will become head of government (in Britain) to take into account the interests of 600 British companies working in Russia," Putin said.
Theresa May will step down as her Conservative party's leader on Friday over her failure to take Britain out of the European Union on time, but will stay on as caretaker premier until a successor is chosen. —AFP