Mr. Bush prodded the international community to stand firm against the nuclear ambitions of Iran and North Korea. He said that despite past disagreements over the U.S.-led war in Iraq, members of the U.N. must unite to help the struggling democracy succeed, according to the Associated Press.
"A few nations, regimes like Syria and Iran, continue to sponsor terror," President Bush told a meeting of the world body in New York. "Yet their numbers are growing fewer, and they're growing more isolated from the world."
But the president warned: "As the 21st century unfolds, some may be tempted to assume that the threat has receded. This would be comforting. It would be wrong. The terrorists believe time is on their side, so they've made waiting out civilized nations part of their strategy. We must not allow them to succeed."
Mr. Bush also voiced criticisms of Russia for invading neighboring Georgia, calling it a violation of the U.N. charter.
"The United Nations' charter sets forth the equal rights of nations large and small," he said. "Russia's invasion of Georgia was a violation of those words."
Iranian leader Mahmoud Ahmadinejad will address the assembly Tuesday afternoon. In interviews with American news outlets Tuesday morning, Ahmadinejad defended his country's nuclear program and blamed the recent problems in global financial markets on U.S. military interventions abroad.
In an interview with NPR Tuesday, Ahmadinejad said his country does not seek confrontation with the U.S: "We do not have confrontations with anyone. The U.S. administration interferes, and we defend ourselves."
President Bush sought to reassure the world body on the handling of the U.S. financial sector shake-up during his speech, voicing confidence that Congress will act in the "urgent time frame required" to prevent a broader problem.
Several world leaders address economic concerns in their speeches Tuesday. Speaking directly after President Bush, French President Nicolas Sarkozy called for a sweeping reform of the global financial system, urging major economic powers to meet before the end of the year to examine the lessons of the crisis.
"Let us rebuild capitalism in which credit agencies are controlled and punished when necessary, where transparency ... replaces opaqueness," Sarkozy said. "We can do this on one condition -- that we all work together in our globalized world."
In opening remarks to the meeting, U.N. Secretary-General Ban Ki-moon urged the international community to confront the financial crisis as well as food and energy price spikes and new outbreaks of war and violence.
"We must do more to help our fellow human beings weather the gathering storm," Ban told world leaders. "I see a danger of nations looking more inward, rather than toward a shared future. I see a danger of retreating from the progress we have made, particularly in the realm of development and more equitably sharing the fruits of global growth."