David Cameron today flatly rejected a call from Russia for the restoration of links between the countries' intelligence agencies despite the ongoing dispute over the Alexander Litvinenko murder.
The Prime Minister also stressed that the Government was not giving up on attempts to extradite the UK's prime suspect in the killing of the dissident five years ago, ex-KGB agent Andrei Lugovoy.
However, he insisted the two governments could still improve business and political ties even though the dispute was no closer to being resolved.
Mr Cameron was speaking at a press conference alongside president Dmitry Medvedev during his visit to Moscow - the first by a British leader since 2005.
Mr Medvedev said the anniversary of the September 11 attacks emphasised the need for countries to co-operate to tackle terrorism.
"In this regard I believe that there is a need to reconstitute the contacts not only between the law enforcement agencies but between the special services," he said.
But Mr Cameron responded: "We haven't changed the arrangements between our security services, which were frozen after the Litvinenko issue.
"That is not being discussed as something that is going to change.
"But I think that we can talk about how we co-operate in terms of combating criminality, and how our police services, our serious and organised crime (agencies) work together in the future."
Mr Cameron denied that the British Government was trying to "park" the Litvinenko case to help thaw relations.
He said the Government still disagreed, but it was possible to move "beyond" the issue.
Mr Medvedev reiterated Russia's position that extraditing Mr Lugovoy was impossible under the country's constitution.
"We all have to learn to respect our legal frameworks," he said through an interpreter. "That will never happen no matter what will be the circumstances."
Mr Medvedev also took a swipe at the UK justice system, saying he had "questions" about the way the courts operate.
"We have many questions about how the legal questions are being resolved in the UK," he added.
Mr Cameron's one-day visit is focusing on strengthening business links and improving conditions for UK firms in the country.
BP chairman Bob Dudley is among 24 senior executives travelling with the premier, and some £215 million of deals have been sealed, creating 500 UK jobs.
However, the leaders' joint appearance was dominated by questions about the poisoning in London of Mr Litvinenko, which sent relations into the deep freeze.
Mr Cameron said there was a "bilateral agenda for Britain and Russia that needs to be progressed, and should be progressed".
Challenged over how he could simply put aside the unresolved murder, he replied: "It's not parking an issue, just recognising there's a disagreement, that hasn't changed... We should work on our relationship beyond it."
Mr Cameron later held talks with Vladimir Putin at his official residence in Moscow.
UK officials have made the extraordinary admission that no minister or senior diplomat has spoken to Mr Putin for four years.
Although currently Prime Minister, he could return to the top job in elections next year.
After shaking hands the two men sat facing each other across a table, flanked by their respective delegations.
"We are very glad to see you and this is the first visit by the PM of Great Britain in the past five years," Mr Putin said through an interpreter.
"I should say the trade and economic development over the past years has been developing very successfully.
"Last year GB was in first place among our trade and economic partners in economic investment.
"Even though the investments in the real sector of the economy are rather modest.
"In any case GB is our old trade and economic partner and we have lots to discuss."
Mr Cameron replied: "Thank you very much for that welcome.
"It's a great opportunity for Great Britain and Russia to try to build a stronger relationship.
"It is good to have the opportunity today.
"The economic relationship in recent years has grown considerably, particularly in terms of imports and exports of goods."