Russia's President Dmitry Medvedev (C) and Britain's Prime Minister David Cameron (R) attend a signing ceremony in Moscow's Kremlin Sept 12, 2011. [Photo/Agencies]

MOSCOW - Russian President Dmitry Medvedev joked on Monday that visiting British Prime Minister David Cameron would have made a very good KGB agent, after Cameron suggested that the Soviet security service tried to recruit him when he was a student.

"I am convinced David would have been a very good KGB agent but in this case he would have never become prime minister of Britain," Medvedev said at a joint news conference at the Kremlin as both leaders laughed.

Cameron earlier tried to break the ice in a speech to students at Moscow State University by recalling how he had first visited Russia in the waning years of the Cold War in 1985 during a gap year between school and university.

"I took the Trans-Siberian Railway from Nakhodka to Moscow and went on to the Black Sea coast. There two Russians - speaking perfect English - turned up on a beach mostly used by foreigners," he said.

"They took me out to lunch and dinner and asked me about life in England and what I thought about politics. When I got back I told my tutor at university and he asked me whether it was an interview. If it was, it seems I didn't get the job!" he said.

When a journalist asked Medvedev later whether Cameron would have made a good KGB agent, Cameron jumped in to say: "The answer to that last question I think is no, let's be clear about that."

The joke was a rare light-hearted moment during Cameron's 24-hour visit because relations between Russia and Britain remain soured by a murder in London that could be drawn straight from a Cold War spy story.

Cameron was making the first visit to Russia by a British prime minister since former Russian spy Alexander Litvinenko died in London from poisoning by radioactive polonium-210 in 2006.

Russia refuses to extradite Andrei Lugovoy, a former KGB bodyguard who is now a lawmaker in the Russian parliament. Britain wants to prosecute him over the killing.

Cameron was meeting later on Monday with Russian Prime Minister Vladimir Putin, himself once a KGB spy.

Cameron first told the story about his suspected brush with the KGB in a 2006 radio interview when he said that the incident raised eyebrows when he was being vetted to become an adviser to the British Treasury in the 1990s.