He told the General Assembly that the United States wanted to work through the Security Council - but warned that military action would be unavoidable if Iraq failed to comply with UN resolutions.
"The Security Council resolutions will be enforced - the just demands of peace and security will be met - or action will be unavoidable. A regime that has lost its legitimacy will also lose its power."
Earlier, Iraq's Foreign Minister Naji Sabri defiantly warned Mr Bush that Iraqis would defend themselves to the death.
'Case against himself'
Mr Bush said Saddam Hussein had proved his contempt for the United Nations and listed all the UN resolutions he considered Iraq to have ignored or broken.
"By his cruelties... Saddam Hussein has made the case against himself," he said.
Bush's demands of Iraq
"Are UN resolutions to be honoured and enforced or cast aside without consequence?" he asked.
The UN itself faced a "difficult and defining moment" over the issue.
He said that should Iraq acquire fissile material, "it would be able to build a nuclear weapon within a year".
He accused Saddam Hussein of allowing members of Osama Bin Laden's al-Qaeda network to be based in Iraq.
"If the Iraqi regime wishes peace, it will immediately and unconditionally foreswear, disclose, and remove or destroy all weapons of mass destruction, long-range missiles and all related material," he said.
Mr Bush's speech brought a mixed reaction around the world.
British Foreign Secretary Jack Straw said it was "a defining moment for the United Nations".
"No-one who heard President Bush's speech could be in any doubt... about the urgency of dealing with the threat posed by Saddam Hussein," he said.
But US Senate Majority leader Tom Daschle said a number of questions still had to be answered before Congress voted to back military action against Iraq.
He said many members of Congress wanted to see the reaction of the international community before authorising use of US forces.
Afghan President Hamid Karzai told ABC TV he was worried that US involvement in Iraq could switch attention away from efforts to eradicate the Taleban and al-Qaeda in his country and to rebuild its infrastructure.
He said he wanted a better life for the Iraqi people but said any American action should be done with the support of the Arab world.
The Iraqi media said Mr Bush was using the UN to promote lies about alleged weapons programmes in Iraq.
Mr Bush "wants to exploit the international body as a tool serving and giving legitimacy to his aggressive schemes against Iraq," said al-Thawra, the ruling Ba'ath Party's newspaper.
Annan warning
UN Secretary General Kofi Annan earlier told the General Assembly that there was no substitute for the UN's "unique legitimacy".
"I believe that every government that is committed to the rule of law at home, must be committed also to the rule of law abroad," he said.
He acknowledged that Iraq had not complied with UN resolutions and urged the country to end its recalcitrance "for the sake of its own people, and for the sake of world order".
"If Iraq's defiance continues, the Security Council must face its responsibilities," he said.
Iraq has reiterated its defiance to any military action. Mr Sabri told Reuters news agency that his countrymen would use all means, even "kitchen knives", to repel an American invasion.
Iraq denies developing weapons of mass destruction.
"We shall never let those Zionists invade our country," Mr Sabri said.
Mr Bush's address came as US Central Command - which oversees the war in Afghanistan and army operations in south-west Asia - announced plans to send 600 of its headquarters' staff to the Gulf state of Qatar, near Iraq, for a training exercise in November.
To back up the president's speech, the Bush administration released a 22-page document recording what it said was "Saddam Hussein's defiance of the United Nations" on Thursday.