During his visit to South Africa, Mr Major rejected parallels between the IRA and the ANC. He said: 'Don't think you can have an amnesty in the UK. In the UK, people are not in jail as political prisoners. They are in jail because they have committed crimes, sometimes murder. They have been sentenced by judicial process. They have to serve their sentences.'
After his talks with President Nelson Mandela, Mr Major was asked whether he hoped one day to hold negotiations with Mr Adams.
'That is not imminent,' Mr Major replied. 'What we are waiting to hear at the moment is confirmation that . . . they have given up violence for good.
'I am waiting for them to make that clear. I am not hung up on them using any particular set of words to do so. I want it unambiguously clear so there is confidence amongst the people who in due course need to sit down and talk to Sinn Fein they are not going to suddenly pick up arms and renew the violence again.
'They can do it how they wish, in the words they wish, but I think those people who will have to negotiate with them and the people who live in Northern Ireland will want to have that assurance. I think they are moving towards it and I am very grateful, I am pleased.'
Once they had cleared that hurdle, negotiations would begin on bringing them into the talks. 'They will then sit around the table and have the political talks proper. Whether Mr Adams represents Sinn Fein is a matter for Sinn Fein. He may well be there.'
His failure to rule out meeting Mr Adams will annoy some unionists who have accused the government of a secret deal behind the IRA ceasefire, a charge Mr Major has denied. Mr Major has been assured by President Clinton that he will not meet Mr Adams on his next visit to the US. Albert Reynolds, the Irish Prime Minister, has already met Mr Adams.
The Prime Minister declined to say his success on Ulster could be a turning point for his fortunes. 'No wise politician ever says that. Politics is a series of man-traps. I think there will be a whole series of things . . . where we are beginning to see the fruits.'
Dick Spring, the Irish Foreign Minister, is to meet Tony Blair today with Dublin seeking reassurance that Labour still supports unity by consent for Ireland.
Mr Spring, leader of the Irish Labour Party, has yet to meet the UK's new Labour leader and is taking advantage of a breakfast meeting before the first session of the Anglo-Irish conference since the IRA ceasefire.
That meeting, with Sir Patrick Mayhew, will be the first chance to consider the economic consequences of the ceasefire, while the Irish will also want to hear how much closer the British government has moved to accepting the Irish government view that that the ceasefire is permanent.