Sir Norman said the Cabinet was united over its opposition to the Social Chapter of the Maastricht treaty, on which the Government was defeated last week, and John Major's strategy for tabling an immediate confidence motion.
He added: 'If someone inside the cabinet has total reservatiobns he has a duty to look to his own position. There is nothing new about that.'
However, Mr Major's unguarded remarks to Michael Brunson, the political editor of ITN, in the aftermath of Friday's confidence vote, threatened to break the uneasy truce over Maastricht by rubbing salt in the rebels' wounds. It will also test the loyalty of his three Cabinet colleagues who actively lobbied the rebels last week not to vote against the Government.
Mr Major, apparently not realising he was being recorded, said after an interview for ITN at Downing Street that he had not sacked dissidents within the Cabinet because he did not want three more of the 'bastards' on the backbenches.
'The real problem is one of a tiny majority. Don't overlook that. I could have all these clever, decisive things which people wanted me to do - but I would have split the Conservative Party into smithereens. And you would have said I had acted like a ham-fisted leader,' the Prime Minister said.
Mr Brunson then asked why Mr Major had not sacked the Cabinet dissidents, widely regarded as Michael Howard, the Home Secretary; Peter Lilley, the Secretary of State for Social Security; and Michael Portillo, Chief Secretary to the Treasury.
'Just think it through from my perspective,' Mr Major replied. 'You are the Prime Minister with a majority of 18, a party that is still harking back to a golden age that never was and is now invented. You have three right-wing members of the Cabinet who actually resign. What happens in the parliamentary party?'
Mr Major said: 'I could bring in other people. But where do you think most of this poison is coming from? From the dispossessed and the never-possessed. You can think of ex-ministers who are going around causing all sorts of trouble.
'We don't want another three more of the bastards out there. What's Lyndon Johnson's maxim? . . .'
That was seen as a reference to Lyndon Johnson's refusal to sack J Edgar Hoover, the director of the FBI, because it was 'probably better to have him inside the tent pissing out than outside pissing in'. The sound was cut off at that point.
The party chairman yesterday did not deny the remarks, but protested at the way the private conversation had been leaked. He said an inquiry should seek to discover how it was made public.
Sir Norman also offered the rebels an olive branch on the Breakfast with Frost programme, by disowning the basic programme agreed by the European People's Party, which the Tory rebels fear will become the basis for the Tory manifesto for the European elections next June.