No 10 Downing Street released a telex from Mr Clinton declaring that he places 'a high premium on the historic and special relationships between the United States and Britain'.
While the future US president remains too busy assembling his administration to see Mr Major when he visits Washington later this month, Mr Clinton said he hoped to speak to the Prime Minister by telephone and looked forward to 'strong personal relations'.
Neither country, he told Mr Major, could achieve its objectives unless they were closely tied.
The impression of strain between the two over the part Conservative party officials played in boosting President George Bush's re-election campaign has been heightened by Home Office confirmation yesterday that in the closing weeks of the US campaign officials checked records to see if Mr Clinton had applied for British citizenship in an attempt to dodge the draft during the Vietnam war in the 1960s.
That check was made despite a Home Office statement yesterday that official policy is: 'We do not discuss individual applications at all'.
As Labour demanded a full ministerial explanation, officials indicated that the search was undertaken in an attempt to be 'helpful' to a flood of press inquiries following the United States rumours.
Sources first indicated that despite the firm policy of not discussing individuals, guidance could have been given - and indeed appears to have been given to the Washington Post - that no file existed, thus killing the story. Had an application existed, guidance could have been given the other way, sources indicated.
That was later amended by a Home Office spokeswoman to say: 'If we had found any information, it would not have been released without the permission of the individual concerned'.
Tony Blair, Labour's home affairs spokesman, yesterday called for a full explanation from Kenneth Clarke, the Home Secretary, of what he described as 'an extraordinary state of affairs.
'If such personal information is, quite rightly, absolutely confidential and would not have been given out, why was it looked for in the first place?
'To have Home Office officials trawling through Mr Clinton's records at a highly sensitive time in the US election, when Conservative party officials were advising the Republican campaign, and Mr Clinton's actions when he was in Britain were an issue, is very disturbing.'
Any suggestion that such personal information might have been disclosed on a guidance basis was 'completely unacceptable,' he said.
As Mr Blair asked which minister or ministers authorised the search, Home Office sources said that the decision was taken by officials without ministerial involvement.
That was greeted with disbelief by David Winnick, the Walsall North Labour MP, who said it was 'inconceivable civil servants would do anything so politically sensitive without a political instruction.' If they had done so, he asked, had disciplinary action been taken?