Tony Blair challenged the United Nations to "come of age" as he warned of the consequences of failing to unite on tackling terrorism and poverty.
Tony Blair won backing in the fight against terrorism
The UN is meeting in an effort to find consensus on moves to reform the body, as well as tackling poverty.
Mr Blair told the summit more work was needed to stop the spread of nuclear, chemical and biological weapons.
It was now widely recognised the UN could intervene when nations failed their own people, he argued.
In an appeal for unity among the 191 UN member states, the UK prime minister said: "The UN must come of age. It must become the visible and credible expression of the globalisation of politics.
"We work with each other or we suffer in isolation."
Having earlier had backing for his call for international action against those who incite terrorism, Mr Blair said the UN had a key role.
The prime minister said: "The terrorist attacks of the 7 July have their origins in an ideology born thousands of miles from our shores.
"The proliferation of nuclear, chemical and biological weapons will never be halted outside of an international consensus to do so.
"The UN can be the instrument of achieving the global will of the people. It must give leadership on terrorism.
"There is not and never can be any justification, any excuse, any cause that accepts the random slaughter of the innocent. Wherever it happens, whoever is responsible we stand united in condemnation."
Mr Blair also spoke about poverty and the need to fulfil the millennium development goals, to improve life for the world's poorest people.
"Stalking this summer like a spectre are the millennium development goals," he said.
"The struggle against global poverty will define our moral standing in the eyes of the future."
Mr Blair did not directly refer to the genocide in Rwanda, often cited by critics of the UN as one of its worst failures, or the situation in Darfur or Sudan.
But he said it was now recognised that states' sovereignty could be overridden by the UN when people were suffering.
"The United Nations peacebuilding commission must become the means of renewing nations where war and the collapse of proper systems of government have left them ravaged and their people desolate.
"For the first time at this summit we are agreed that states do not have the right to do what they will within their own borders but that we in the name of humanity have a common duty to protect people where their own governments will not."
'Exploiting our weaknesses'
The summit has failed to agree a definition of terrorism.
But the UN Security Council backed a resolution brought forward by the UK calling on all states to outlaw incitement to terrorism.
Mr Blair said terrorism would not be defeated until the UN united in both condemning acts of terror and fighting the "poisonous propaganda" which fuelled it.
He warned: "They want us to believe that somehow it is our fault. That their extremism is somehow our responsibility.
"They play on our divisions... they exploit our hesitations. This is our weakness and they know it - and we must unite against this ghastly game with our conscience."