United Nations ? President Bush, defending his decision to invade Iraq, urged a vast assembly of world leaders Tuesday to stand united with the country’s struggling government and said the proper response to spreading violence “is not to retreat, it is to prevail.”

The country’s prime minister, Ayad Allawi, offered an upbeat assessment after Bush’s speech to the General Assembly of the United Nations, saying, “We are winning, we are making progress in Iraq, we are defeating terrorists,” even as insurgents claimed they had killed a second American hostage in two days.

Of the brutal slayings, Bush said, “We will not allow these thugs and terrorists to decide your fate and to decide our fate.”

Yet in a sign of continuing world unease with the situation, U.N. Secretary-General Kofi Annan — who last week called the war in Iraq illegal because it lacked Security Council approval — warned that the “rule of law” is at risk around the world.

“No one is above the law,” Annan said Tuesday. He condemned the taking and killing of hostages in Iraq, but also said Iraqi prisoners had been disgracefully abused, referring to the U.S. treatment of detainees at Abu Ghraib prison near Baghdad.

Often at odds with the United Nations on Iraq, Bush stood before a hushed General Assembly at the opening session of the 191-nation meeting.

The U.N. appearance gave Bush a world stage on which to demonstrate his foreign policy leadership and defend his Iraq policies, a sensitive political issue because of the relentless violence and the deaths of more than 1,000 American soldiers.

Standing before many allies who refused to send forces to Iraq, Bush said, “There is no safe isolation from terror networks or failed states that shelter them, or outlaw regimes or weapons of mass destruction. Eventually there is no safety in looking away, seeking the quiet life by ignoring the struggles and oppression of others.”

After the speech, Bush brushed aside a bleak National Intelligence Estimate of Iraq’s future that spoke of possibilities ranging from tenuous stability to civil war. Bush characterized the scenarios developed by senior U.S. intelligence officials as “life could be lousy, life could be OK, life could be better. And they were just guessing as to what the conditions might be like.”

Many world leaders hesitated to comment on Bush’s speech. South African President Thabo Mbeki said, “I’m still reading it.” Many European leaders skipped the meeting entirely, sending their foreign ministers instead.

Iraq has been Bush’s dominant theme at the United Nations since the Sept. 11, 2001 attacks, but he softened his speech this year to discuss the “great issues of our time,” like fighting AIDS, human slavery, poverty, the violence in Sudan, corruption and banning human cloning.

But Bush was unapologetic about his decision to invade Iraq, and he linked the chaos and violence there to the more politically popular war on terrorism, saying terrorists believe “suicide and murder are justified … . And they act on their beliefs.” He cited recent terror acts, including the deaths of children earlier this month in a Russian school.