Meeting with British Prime Minister Gordon Brown on the sidelines of a G8 summit on Monday, Dmitry Medvedev urged efforts "to return to the level of relations the two countries enjoyed a few years ago."
In an interview with Vesti 24 channel, Konstantin Kosachev said however that this merely meant that "we should return to the position of observing international and national law."
Ties between Moscow and London have plunged to a post-Cold War low over a series of disputes, including Russia's refusal to extradite London's chief suspect in the 2006 poisoning of Kremlin critic and security service defector Alexander Litvinenko, the ensuing closure of British Council offices in Russia, and a shareholders' dispute in the joint oil venture TNK-BP.
Moscow has refused to extradite Andrei Lugovoi, saying its Constitution prohibits this. Russia cited tax and other violations behind the closure of the regional offices of the British Embassy's cultural arm. London insisted the move was political.
Officials in Russia also said the government would not get involved in the current TNK-BP conflict, in which British oil major BP and its Russian billionaire co-owners have clashed over strategy, management and control of the company, Russia's third largest oil producer.
Medvedev told Brown on Monday that the Russian government did not consider interference in the TNK-BP dispute possible as "this is an issue between two companies."
"I am certain that by inviting Gordon Brown to return relations to normal, the Russian leader meant a return to appropriate legal attitudes," the lawmaker said.