The idea received general approval from Nato ambassadors in Brussels yesterday. Mr Yeltsin has warned of a "cold peace" if Nato enlarges to take in former Warsaw Pact countries. Poland, the Czech Republic, Hungary and Slovakia are the main contenders.
There is deep concern that relations have deteriorated badly over the last year, beyond the public rows. Some Nato officials fear that, despite efforts to build bridges with Russia and, in particular its military, the most important officers still have little concept of Nato beyond that learnt in the Cold War.
Mr Clinton's letter will set out a wider relationship between Russia and the West. However, it does not propose a new Nato-Russian security agreement, according to Nato sources, but refers to two existing agreements - one setting out Russia's participation in the Partnership for Peace, the other for a broader dialogue, which Russia agreed but then did not sign.
Russia has invited Mr Clinton to a special summit on 8 May to mark the end of the Second World War in Europe. Such a meeting could cement closer ties and advance the creation of a new security architecture for Europe, a cherished goal of the Clinton administration.
Nato diplomats were not shown the Clinton letter, but were briefed and given the chance to make suggestions about the line to be taken.
The exercise goes back to a meeting between Warren Christopher, the US Secretary of State, and Andrei Kozyrev, the Russian Foreign Minister, last month. Russia is expected to reply with its own ideas, and, it is hoped, with a date when it will sign the two agreements.
However, in the longer term there may be a more formal agreement between Nato and Moscow, according to some diplomats and officials.
The idea has been frequently discussed but it may take until later this year to emerge as a fully-fledged proposal. The concept of a new East- West agreement stirs some deep fears, not least in those countries in central Europe that may not come into the alliance.
Nato is conducting a study of the implications of enlargement which should be finished this year. The US wants this study to lead straight on to decisions on who should join and when.
Last year European members of Nato were worried that the US was trying to accelerate the entry of new members. The US decision to pass the letter through Nato may have been intended to reassure the European members no over-hasty steps were being taken.