At his monthly press conference in Downing Street Thursday, he set out the challenges facing the government, ranging from nuclear power to anti-social behaviour.
Asked whether he was in the running for the post of secretary general, he said ''I am not going for the UN job.''
Tony Blair says he will stay on
Former Foreign Secretary Jack Straw had told The Spectator this week that Blair would go ''well before the next election'' and would then take ''a very important role on the world stage.''
Asked about Straw's comments, the British Prime Minister said ''If you do not mind, I have said all I intend to say on this subject. I think the most important thing for us as a government is to get on with the job.''
There was a lot to do, he said. Asked whether Straw was his choice to replace John Prescott as the deputy prime minister, he said ''I would rather see an end to my having to answer the questions.''
The pressure on Blair to bring forward his departure was maintained by former cabinet minister Chris Smith, who called on him to resign next year. The former culture secretary, now Lord Smith of Finsbury, said the British Prime Minister should not serve a full third term because his presumed successor Mr Gordon Brown would need enough time to establish himself before a general election.
Clinton backs Blair as UN chief
In an interview with the political website ePolitix.com, Lord Smith said under David Cameron, the Tories were ''a very real threat.''
''What is undoubtedly needed is an orderly transition in the course of the next year in order for Mr Gordon Brown, who I very much hope will become the next leader of the party and prime minister, to have enough time, having become prime minister, to establish his own style, his own agenda, his own priorities in the public mind before he then fights an election. I would like to see it happening at a sensible point," he said.
Lord Smith warned both the leaders camps and those jockeying to replace Prescott not to engage in a damaging war of words before the transition.
But those close to Blair hope he can get through to the party conference in the autumn without further serious mishap, although there is a growing view in the party that he will go soon after his 10th anniversary as Prime Minister next May.
Straw said he had ''nothing further to add'' and refused to be drawn on Blair's likely departure date or his own ambitions to become deputy leader, when he briefed political journalists for the first time in his new role as the Leader of the House.
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