The gathering of the Group of Seven leading industrialised nations is being held at the suggestion of Mr Yeltsin, who faces a strong Communist challenge in June's presidential election.
Although western diplomats admit the summit, which comes less than a week before the 10th anniversary of the Chernobyl disaster and covers a pot-pourri of issues on nuclear safety and security, is unlikely to produce any historic developments, they have been touting it as an important opportunity to forge closer relationships over critical nuclear-related issues.
Of these, there is no shortage. The G7 (or G8, as Russia prefers) will discuss, and almost certainly accept, proposals for their security services to co-operate more closely in efforts to clamp down on the theft and smuggling of fissile material, reducing the risk that weapons-grade materials could fall into the hands of terrorists.
It will endorse an agreement to shut down Chernobyl by the end of the century, and discuss closing similar ageing RMBK reactors - of which there are 15 in the former Soviet Union - and tightening controls on others. Officials say there will be talks over the disposal of nuclear waste and completing a comprehensive test ban treaty. Russia can also expect to be under renewed pressure to sign the amended London Convention which bans the dumping of radioactive waste at sea.
But as Moscow spruced herself up for the event, a ground swell of criticism has surfaced among independent nuclear experts and environmentalists, who allege the summit does not go far enough. They claim it fails to tackle several of the most important issues - for example, the ratification of Start-2.
"Instead of a state dinner, the G7 and Russia should gather for a prayer breakfast," said Dr Tom Cochran, a senior scientist with the US Natural Resources Defence Council, one of a task force of international non-governmental organisations in Moscow. The summit's safety programme is "far too little to prevent another Chernobyl-style catastrophe", he warned.
Similar complaints have been raised by Greenpeace and other environmental groups. The more cynical have not failed to remark on the irony of the summit's co-chairmanship - Boris Yeltsin, whose military forces have dumped some of the most hazardous waste on the planet, and Jaques Chirac, still "public enemy No1" among environmentalists over France's nuclear tests in the Pacific.
This is unlikely to bother Mr Yeltsin, who has reportedly made it clear to his guests - including Mr Clinton - that he wants the lion's share of the limelight as he tries to overtake his chief rival for the presidency, the Communist leader Gennady Zyuganov.
Mindful that they may one day have to deal with him, American officials have, however, invited Mr Zyuganov to a meeting with Mr Clinton.Reuse content