The Russian leader, Dmitry Medvedev, arrived in Japan for the summit with weapons on his mind. He met George Bush for the first time since becoming President, seeking assurances on the proposed US anti-missile shield.
The Russian camp claims promises made by Bush in Sochi in April have not been kept and the positions of Moscow and Washington remain divergent.
Moscow says the US is not taking its concerns seriously and it wants the matter sorted out before President Bush leaves office in January.
The Bush administration is said to have offered Moscow control over anti-missile shield sites in eastern Europe and co-operation on the project in general back in April. But little progress has been made since then.
Medvedev was also said to be keen to discuss the START treaty limiting nuclear weapons in each country which expires next year.