The Prime Minister showed his frustration with divisions in the 191-member body by warning fellow world leaders that they would only defeat terror when their determination and unity matched the single-minded fanaticism of the terrorists.

Speaking to the UN as news came through of fresh carnage in Baghdad, Mr Blair said that terrorists would continue to exploit international hesitation.

He told the Security Council: “Terrorism will not be defeated until our determination is as complete as theirs, our defence of freedom as absolute as their fanaticism, our passion for the democratic way as great as their passion for tyranny.”

Although he won unanimous support for a new UN resolution urging all nations to outlaw incitement to terrorism, the UN General Assembly was unable even to agree a definition of terrorism in its anniversary declaration due out today.

Strong language in an earlier draft stating that “deliberate and unlawful targeting and killing cannot be justified or legitimised by any cause or grievance” was purged from the final declaration.

The British-sponsored UN resolution passed yesterday calls on all countries to comply with the UN’s counter-terrorism committee and to deny safe haven to terrorists and those who incite terror. It also called on nations to “prevent the subversion of educational, cultural and religious institutions by terrorists and their supporters” — a reference to madrassas being used in Pakistan to school extremists.

But the resolution was considered a sticking plaster on the General Assembly’s failure to define terrorism, because it lacked any talk of sanctions or compulsion. It followed the filleting by countries, including Pakistan and Syria, of strong measures on terror from today’s declaration.

Mr Blair did not disguise his impatience at the weak message being sent out from the UN headquarters in New York just days after the fourth anniversary of 9/11. He said: “Terrorists want us to believe that terrorism is somehow our responsibility. They play on our divisions. They exploit our hesitations. This is our weakness and they know it.”

He rejected charges that Iraq was the root cause of extremist Islamic terror. “The obstacle is terrorism, their victims are largely Muslim. . . They use Iraq to divide us, just as they use Afghanistan where again their terror is the obstacle to democracy. . . The root cause is not a decision on foreign policy, however contentious. It is a doctrine of fanaticism.”

Mr Blair concluded: “We must unite to uproot it by co-operating on security, by taking action against those who incite, preach or teach this extremism wherever they are, and by eliminating our own ambivalence by fighting not just their methods but their motivations, their twisted reasoning, their wretched excuses for terror.”

President Bush also seemed to show frustration with the shortcomings of the UN declaration. He said: “There is no safety in running away. Either hope will spread or violence will spread. . . terrorists must know that wherever they go, they cannot escape justice.”

Downing Street was keen to emphasise the importance of the unanimous 15-member Security Council vote on measures to combat incitement to terror, against the weak UN General Assembly declaration. The nations most opposed to UN action to prevent the killing of civilians were not represented on the Security Council.

Mr Blair’s spokesman said: “The Security Council is the decision-making body of the United Nations. Its decisions have the force of law within the UN.”

The Prime Minister later held a meeting with President Musharraf of Pakistan, one of the nations held responsible for watering down the UN’s rhetoric on terrorism.

But Downing Street emphasised that Mr Blair was pleased with Pakistan’s actions against terrorism, including a clean-up of madrassas.

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