The US intervention, which may have been critical in defeating the coup, has been kept secret to avoid the accusation that Washington was interfering in Russian affairs. It also started a row between the White House and the code-breaking National Security Agency, which strongly objected to revealing to Moscow that its most secure communications were compromised.
The degree of support for Mr Yeltsin from the American security services is disclosed by Seymour Hersh, one of the United States' best-known investigative journalists, in the forthcoming issue of the Atlantic Monthly magazine. It is likely to fuel allegations by Mr Yeltsin's opponents that he took power thanks to American support.
As soon as the coup started on 18 August 1991, the NSA, America's largest intelligence organisation, was able to decrypt conversations between the coup's two leaders, Vladimir Kryuchkov, chairman of the KGB, and Dmitri Yazov, the Defence Minister, taking place over a supposedly secure landline. President Bush ordered the information to be given to Mr Yeltsin but, fearing Russian reaction if word of American interference leaked out, broke the law by not telling Congress.
The information was of critical significance to Mr Yeltsin at a moment when both sides in Moscow were wooing various military commanders across the Soviet Union. Mr Yeltsin knew exactly who supported the coup and who opposed it.
An American specialist from the US embassy was sent to Mr Yeltsin's office in the Russian parliament building to make sure that his own communications system was secure.
'The Minister of Defence and the KGB chief were using the most secure lines to reach the military commanders,' a US official involved in the operation said. 'We monitor every major command, and we handed it to Yeltsin on a platter. It demonstrated to the Soviet commanders that we can read it all - that we can penetrate it.'
The NSA's ability to decrypt what Soviet military commanders - and their Russian successors - said over their communications system is probably the most significant intelligence achievement since Britain broke Germany's Enigma codes during the Second World War.
William Odom, head of the NSA until 1988, says the transfer of such highly classified information would lead to 'a terrible, terrible trade-off . . . Now the Russians know what I know. That is such a huge loss for the future.'
However, General Odom admitted that it was President Bush's right to decide what to do with such intelligence information, adding: 'There would be those who would think saving Yeltsin is worth it.'
In fact on 14 August 1991 - only four days before the attempted coup in Moscow - President Bush had signed an amendment to the law making it illegal for him not to tell House and Senate Intelligence Committees in secret session about covert action such as that in support of Mr Yeltsin.
Mr Bush and his aides reportedly decided to flout the law because they feared that Congress might balk at helping Mr Yeltsin because of the possible Russian reaction.
There is no information about how the NSA succeeded in penetrating Soviet military communications, or counter-measures taken since by Russian commanders to keep their conversations secret. During the final years of the Soviet Union many secrets, formerly closely held, were sold to Western intelligence services.
Mr Yeltsin was clearly grateful to Presidents Bush and Clinton for the support the US gave at a critical moment in his political fortunes, but he also has an incentive to prevent the same breach in security happening again.
Mr Hersh says: 'The US intelligence community may no longer be in a position to have advance warning of momentous events inside Russia - as it had months before the coup that brought Yeltsin to power.'
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