Leaders from the Group of Eight major industrialized powers will meet for three days in Hokkaido, northern Japan, for talks focusing on climate change, sustainable energy, food security and African development.
Russian President Dmitry Medvedev is due to hold a bilateral meeting with British Prime Minister Gordon Brown on the sidelines of the summit.
"We hope Britain will signal its willingness to improve relations with Russia," the diplomat told the press.
Relations between London and Moscow have deteriorated since the dispute over Russian businessman and MP Andrei Lugovoi, British police's chief suspect in the case of poisoned defector Alexander Litvinenko.
The two countries engaged in tit-for-tat expulsions of diplomats after Russia refused to extradite Lugovoi citing the Constitution. The Russian authorities have also closed two British Council offices.
Nonetheless, Russia and the United Kingdom are seeing their bilateral trade rise, and Britain was the leading foreign investor in the Russian economy last year.
Also ahead of the forum, Russia warned Japanese public and political institutions against raising its territorial dispute with Japan over the Kuril Islands.
The South Kuril Islands, known in Japan as the Northern Territories, were annexed by the Soviet Union after World War II and the dispute has prevented the two countries from signing a peace deal.
"Japan's public organizations have raised the problem of what they call Northern Territories in the run-up to the summit, with the tacit support of the authorities," a Russian Foreign Ministry official told reporters Wednesday.
"We believe this is politically incorrect, especially since Japan is the host country for the summit," he said. "Bilateral problems are not in the traditions of the summit."
