Gordon Brown has been welcoming a succession of leaders to No 10
Gordon Brown has met Russian President Dmitry Medvedev for talks ahead of Thursday's G20 summit of world leaders.
Mr Brown has admitted "difficulties" in UK-Russian relations but said the two can work together on issues ranging from Iran to nuclear proliferation.
Relations between London and Moscow deteriorated in 2006 after the murder of Alexander Litvinenko in London.
Earlier in Parliament, Mr Brown was urged to press the Russian leader on his country's human rights record.
Labour MP Gisela Stuart said a recent raid by Russian authorities against a human rights group were extremely worrying.
Mr Brown said he had brought up areas of difference between the two countries at past high-level meetings and would do so again on Wednesday.
"There have been difficulties in the relationship between Britain and Russia," he acknowledged.
"But it is also important to recognise we want Russia to work with us on a Middle East peace settlement, in dealing with the problems of Iran and so we can achieve multilateral disarmament and make sure the nuclear non-proliferation treaty works.
"These are all issues where I believe we can also work with Russia."
UK-Russian relations reached their lowest point in many years in 2006 after former KGB agent Alexander Litvinenko, a fierce critic of the Russian government who was granted asylum by the UK, was poisoned in London.
Russia refused to extradite the chief suspect in the case, leading to tit-for-tat expulsions of diplomats from both countries.
The UK was also critical of Russia's military action against Georgia last year and has raised concerns about its energy policy.
But there is hope of better relations on the back of efforts by the new US administration to seek improved ties with Moscow.
Washington has talked of a fresh start in relations and on Wednesday, the US and Russian presidents agreed to begin talks on a new treaty to reduce nuclear warhead levels.
Gordon Brown met a host of world leaders on Wednesday including US President Obama and Indian prime minister Manmohan Singh.