UNITED NATIONS — President Bush, who once warned that the United Nations was in danger of becoming irrelevant, said today that multinational organizations are now “needed more urgently than ever” to combat terrorists and extremists who are threatening world order.

In his eighth and final speech to the U.N. General Assembly, Mr. Bush said the international community must stand firm against the nuclear ambitions of North Korea and Iran. He said that despite past disagreements over the American-led war in Iraq, members of the U.N. must unite to help the struggling democracy succeed. And he scolded 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.”

Mr. Bush, who has had a testy relationship with the U.N. which he says has been slow to address global problems, called on the U.N. to focus more on results and aggressively rally behind young democracies like Georgia, Ukraine, Lebanon, Afghanistan and Liberia.

Mr. Bush said that instead of issuing statements and resolutions after terrorist attacks, the U.N. and such organizations must work closely to prevent violence. Every nation has responsibilities to prevent its territory from being used for terrorist, drug trafficking and nuclear proliferation, he said.

Mr. Bush, who ordered the American-led invasion of Iraq in 2003 without the U.N.’s blessing, said: “The United Nations and other multilateral organizations are needed more urgently than ever.” His farewell address, however, comes at a time when many multilateral diplomatic missions Mr. Bush has championed are stalled. North Korea is backing away from pledges to abandon nuclear weapons. A Palestinian Arab-Israeli peace pact before Mr. Bush leaves office is unlikely. Violence is flaring in Afghanistan and Pakistan. Iran continues to pursue its nuclear work in defiance of international demands.

Throughout Mr. Bush’s speech, the hard-line Iranian President, Mahmoud Ahmadinejad, who has vowed that Iran’s military will “break the hand” of anyone targeting the country’s nuclear facilities, sat in his seat and smiled and waved to people in the chamber. At one point during Mr. Bush’s 22-minute talk, Mr. Ahmadinejad turned to someone at his side and gave a thumb’s down.

Mr. Bush insisted that while regimes like Syria and Iran continue to sponsor terror, “their numbers are growing fewer, and they’re growing more isolated from the world.”

But he 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.”

The 21st century needs a bold and effective United Nations, he said.

“Where there’s inefficiency and corruption, it must be corrected. Where there are bloated bureaucracies, they must be streamlined. Where members fail to uphold their obligations, there must be strong action,” Mr. Bush said.

He called for an immediate review of the U.N. Human Rights Council; a stronger effort to help the people of Burma live free of repression; and more pressure on the government of Sudan to uphold pledge to address violence in Darfur.

Mr. Bush’s appearance at U.N. headquarters was overshadowed by the American financial crisis that has rippled through world markets. Trying to reassure world leaders that his administration is taking decisive action to stem market turmoil, Mr. Bush said he is confident that Congress will act in the “urgent time frame required” to prevent broader problem. But he did not ask other nations to take any specific actions.

Before his speech, Mr. Bush met with President Zardari of Pakistan to discuss the weekend bombing of the Marriott hotel in Islamabad and American military incursions into Pakistan targeting militants using remote areas of the Muslim nation to launch attacks in neighboring Afghanistan and elsewhere. Mr. Bush expressed sorrow for the victims of a deadly truck bomb that devastated a Marriott hotel in Islamabad and acknowledged tensions over U.S. military incursions into Pakistani territory.

Pakistan is under growing pressure from the America to act against Al Qaeda and Taliban insurgents along its border with Afghanistan, a staging ground for attacks against coalition troops in Afghanistan and bombings in Pakistan. Pakistan accuses America of violating its sovereignty.

“Your words have been very strong about Pakistan’s sovereign right and sovereign duty to protect your country, and the United States wants to help,” Mr. Bush said about the incursions, which have caused a rift in U.S.-Pakistan relations.

On the sidelines of the U.N. General Assembly, Mr. Bush attended a meeting on food security, had lunch with a group of political dissidents and met with Presiden Museveni of Uganda — a meeting that the White House said was added at the last minute to discuss the Lord’s Resistance Army led by Joseph Kony, who has led a brutal 21-year insurgency in northern Uganda.

This evening, Mr. Bush is co-hosting an Iraq coalition meeting with President Talabani of Iraq for those countries that participated in the American-led coalition in Iraq. Both leaders will deliver remarks that will underscore the significance of a more stable and prosperous Iraq for a more hopeful future in the Middle East.