David Cameron has vowed to being Alexander Litvinenko's killer to justice during a landmark trip to Russia, aimed at boosting trade ties.

Speaking at a joint press conference in Moscow with Russian President Dmitry Medvedev on Monday, the prime minister insisted: "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".

But Medvedev said while “everyone must respect their country’s fundamental law,” the prime suspect in the case - Andrei Lugovoi - would never be extradited from Russia.

Lugovoi, an ultra-nationalist MP accused by British prosecutors of murdering Litvinenko, earlier challenged Cameron to meet him in Moscow, but only to discuss UK-Russia relations.

He told the Daily Telegraph Britain's interest in the murder of Litvinenko, an outspoke critic of the Kremlin and former Russian spy, was "pitiful.

"My message to David Cameron is: Stop politicising the situation, stop raising this question at a high level with Russian politicians, and move on," he told the paper.

He also reiterated claims that MI5 and MI6 were involved in the murder and the case against him.

Lugovoi, 44, has reportedly not left Russia since 2006 for fear of being arrested. Russia has also complained about the lack of evidence against him.

Speaking to the Huffington Post UK, Alexander Goldfarb, Litvinenko's friend and a campaigner for justice over his death, said:

"Lugovoi will never be extradited because he will tell who sent him on this mission and who gave him the poison and Russia does not want that."

"The visit in itself is not a bad idea," Goldfarb added. "Everyone understands that there are reasons for trade, especially with the global situation in Libya and Iran. Trade is trade but Britain should be careful...

"What is disappointing is that Cameron is meeting Putin. Nobody has met with Putin for four years and everyone knows he is involved. Politically this looks like an endorsement of Putin.

"It seems like the statue for limitation for murder is four years. When all is said and done a British citizen has been murdered in Britain and this turnaround is a total contradiction to British Tradition. What is wrong is this softening attitude towards Putin. As a politician he is the epitome of everything that is wrong."

Cameron's trip is the first by a British prime minister since Tony Blair's visit in 2005. Relations have been strained since the 2006 murder of Litvinenko. The former KGB agent died from radioactive poisoning, believed to have taken place in a London hotel.

Sir Malcolm Rifkind, blogging in the Huffington Post UK said it was vital to maintain the UK's commitment to the rule of law and the freedom of the judiciary by continuing to bring up the Litvinenko case.

Despite the differences, Cameron is insistent that a better relationship can be forged nevertheless.

He said the "tit-for-tat culture" between Russia and Britain had to end. To work through the diplomatic froideur surrounding the Litvinenko case, Cameron said he was taking the approach that "we need to keep working for an honest and open dialogue to address them candidly".

For the sake of the British economy, if nothing else, a thaw in relations is desirable.

Cameron is hoping to do £215m worth of deals on his trip. He is being accompanied by two dozen British businessmen to talks on Monday. Cameron will need to smooth out tensions in the wake of BP's offices being raided, as well as the wider diplomatic difficulties.