With John Prescott, Labour's employment spokesman, and possibly Margaret Beckett, the acting leader, expected to enter the contest this week, Mr Blair is making it clear that unsuccessful challengers would not be punished for opposing him.
His supporters say there is no question of unsuccessful candidates being cold-shouldered or excluded in the way that Bryan Gould was by John Smith after his unsuccessful challenge for the leadership and deputy leadership nearly two years ago. Mr Blair is stressing that his relationship with Mr Prescott, his most likely rival, is good.
Mr Blair, shadow Home Secretary, and clear favourite in the contest, is telling colleagues that the task of the next Labour leader will be to build on John Smith's legacy and that the party's position across the left-right spectrum of policies is close to where he wants it.
When leadership campaigning formally begins after this week's European elections, Mr Blair's agenda is expected to focus around reforms of the party machinery - rather than its constitution - and the creation of a clearer message which would include, rather than exclude, southern voters.
His reassurances about the limits of 'modernisation' come amid growing evidence that the Labour left will ensure a contest takes place. At a dinner for Labour activists on Friday, John Prescott reinforced the view that he intends to stand for the leadership. He said: 'We need a proper debate about leadership, in humour and in comradeship, about principles and what really matters.'
Allies of Mrs Beckett say she too will contest the top job with a powerful coalition of women supporters, activists, left-wingers and MPs who believe Mr Blair to be too inexperienced. One supporter said: 'People have forgotten in all this that she is the only one of the potential candidates who has been a minister and a whip in a Labour government'.
For Mrs Beckett the decision is difficult because, should she run for leader, her position of deputy leader would be threatened. Pressure to run has grown because of her high profile as acting leader. The voting system allows her and Mr Prescott to run without hurting each other. Robin Cook, is still undecided on whether to run.
Mr Prescott's campaign is likely to focus on a clearer definition of his objective of full employment. Mr Blair's economic policy is likely to offer sharp contrast to Mr Prescott's; he believes that Labour needs a clearer identity but argues that it should be forward-looking rather than harking back to the spirit of the 1945 government.
'Persil' Blair, page 6Reuse content