Cameron rejects Russia security call over Litvinenko
David Cameron has rejected a call by Russia to restore links with its security services, which were frozen after the Alexander Litvinenko murder.
Relations between the UK and Russia have been strained since the Russian dissident's death in London in 2006.
The PM said in Moscow the UK would continue to challenge Russia's refusal to extradite the prime suspect.
But he said his one-day trip - the first talks there by a UK leader since 2005 - had improved trade links.
During a news conference with Russian President Dmitry Medvedev, he said they had agreed to increase co-operation in areas including commerce, technology and international issues.
Mr Medvedev called for the two countries to "reconstitute the contacts not only between the law enforcement agencies but between the special services".
However, 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."'Difficult issues'
The prime minister later met Russian counterpart, Vladimir Putin, who had not held substantive discussions with a British minister or official for more than four years as a result of the diplomatic row over the Litvinenko case.
Mr Putin said trade between the nations was "developing very successfully".
Despite all the pomp and ceremony, all that has really changed is that the British and Russian prime ministers are talking again.
On the murder of Alexander Litvinenko, the two sides have agreed to disagree.
On trade, Britain and Russia will continue to pursue what was already a vigorous business relationship. Despite all the difficulties of the last few years British companies have remained among the biggest investors in Russia.
On counter-terrorism, David Cameron maintained the British position that there would be no co-operation with the FSB (one of the successors of the KGB) because of the unresolved Litvinenko poisoning.
But having a proper relationship with Vladimir Putin after four years of silence is an important improvement for the British. Because many people believe he is still the most powerful man in Russia.
Mr Cameron had earlier admitted in a speech at Moscow State University that there remained "difficult issues that hamper mutual trust and co-operation" between the UK and Russia.
"We still disagree with you over the Litvinenko case. Our approach is simple and principled - when a crime is committed, that is a matter for the courts," he said.
The prime minister said victims and their families had a "right to justice".
"We can't pretend these differences don't exist. We need to keep working for an honest and open dialogue to address them candidly," he said.
"But, at the same time, we have a responsibility to recognise the many ways in which we do need each other, to end the old culture of tit for tat and find ways for us to work together to advance our mutual interests."
Mr Cameron spoke in Russian when he told his audience of students: "We are stronger together."
Asked by the BBC's James Landale whether the Litvinenko issue had been "parked" in the interests of trade, Mr Cameron said: "I'm not downplaying it in any way. It remains an issue between Britain and Russia.
"But I don't think that means we freeze the entire relationship."
Mr Medvedev said the legal traditions of different countries should be respected and that under the Russian constitution it was impossible for a Russian citizen to be extradited to a foreign country to stand trial.
"This will never happen whatever the circumstances," he said.'Not complete thaw'
BP chairman Bob Dudley is among 24 senior executives from the UK in the travelling party. The visit is expected to result in £215m of deals, creating about 500 jobs in the UK.
Mr Putin, who could take over at the Kremlin again after elections next year, told Mr Cameron: "We are very glad to see you and this is the first visit by the PM of Great Britain in the past five years.
"Trade and economic development over the past years has been developing very successfully."
BBC Moscow correspondent Daniel Sandford said although the trip was a sign of a defrosting of relations, "it is not a complete thaw".
Mr Cameron later met six human rights activists including Oleg Orlov - a campaigner recently acquitted in a slander case against Chechen leader Ramzan Kadyrov - and Dmitry Muratov, editor of Novaya Gazeta, the newspaper for which Anna Politkovskaya reported before her murder in 2006.
Telling them he had raised the Litvinenko case, he added: "Having good relations doesn't mean sweeping problems under the carpet, it means talking about them."
Mr Litvinenko's widow, Marina, told the BBC's World Today programme she wanted to see those responsible for her husband's death brought to justice because until then "we will not have a normal progress of the relationship between these countries".
Mr Litvinenko, an outspoken Kremlin critic and former security official who had moved to the UK, was fatally poisoned with radioactive polonium-210 in 2006. His death led to both the UK and Russia expelling diplomats.
Moscow has refused a long-standing request from the UK to extradite the prime suspect in the case, Andrei Lugovoi. He is a former KGB officer who is now a member of the Russian parliament and has always denied involvement.
Ahead of the visit, in a letter to the Sunday Times, the prime minister was urged by four former foreign secretaries to challenge President Medvedev over a perceived failure to protect business against corruption and to address the Litvinenko issue.