President Bush on Wednesday called on the world's leaders to continue the fight against terror and help to rebuild Iraq, saying that while some nations may not have faced attacks on their soil, they "still shared in the sorrow."

At the opening meeting of the 60th session of the U.N. General Assembly's world summit in New York, Bush listed 14 nations — Tunisia, Indonesia, Kenya, Tanzania, Morocco, Israel, Saudi Arabia, the United States, Turkey, Spain, Russia, Egypt, Iraq and the United Kingdom — as being direct victims of terror in recent years.

He added that others such as Australia, whose citizens were killed in Indonesia, and Italy, which saw some of its people killed in Egypt, have also faced the impact of unfettered violence.

"No nation can remain isolated and indifferent to the struggles of others," Bush said. "The threat passes easily across oceans and borders and can threaten the security of any peaceful country.

"And those who have not seen attacks on their own soil have still shared in the sorrow. ... The lesson is clear. There can be no safety in looking away or seeking the quiet life by ignoring the hardship and oppression of others."

While offering to reduce international trade barriers and fight global health problems during his far-reaching speech, the president, as he has before, stressed that rebuilding Iraq is key to international stability.

"Democratic nations respect private property, free speech and religious expression. ... And democratic nations contribute to peace and stability. ... For those reasons, the whole world has a vital interest in the success of a free Iraq, and no civilized nation has an interest in seeing a terrorist state emerge in that country," Bush said. "This is a shining opportunity."

Bush also thanked member nations for their assistance and compassion in regard to Hurricane Katrina (search), which two weeks ago devastated the Gulf Coast states of the United States. He said more than 115 nations have pledged help along with nearly a dozen international organizations.

Like the global response to the Indian Ocean tsunami of last December, international reaction to the hurricane "just shows that the world is more compassionate and hopeful when we act together."

In a quietly received speech that touched on everything from AIDS in Africa to the Millennium Challenge Accounts that support democratically evolving nations, Bush pressed the 191-member body to help developing countries improve their economies, secure human rights and permit freedom of religion. He added that for the world body to help the global community, it must also be free of corruption.

"The United Nations was created to spread the hope of liberty and to fight poverty and disease and to help secure human rights and human dignities for all the people of the world," Bush said.

"To help make these promises real, the United Nations must be strong and efficient, free of corruption and accountable to the people it serves. The United Nations must stand for integrity and live by the high standards it sets for others."

Bush pressed for Security Council approval of a resolution calling on all nations to take steps to end the incitement of terrorist acts. The 15-member council later adopted the resolution by voice vote.

Bush asked nations to agree to prosecute and to extradite anyone seeking radioactive materials or nuclear devices.

"We must send a clear message to the rulers of outlaw regimes that sponsor terror and pursue weapons of mass murder: You will not be allowed to threaten the peace and stability of the world," Bush said. "Confronting our enemies is essential, and so civilized nations will continue to take the fight to the terrorists."

Later Wednesday morning, the Security Council passed resolutions 1624 and 1625, resolutions that respectively aim to disrupt the planning of terror attacks and minimize armed conflicts in Africa.

"Terrorism and armed conflict are not only threats to our security, they're the enemies of development and freedom for millions. To help ensure the 21st century is one of freedom, security and prosperity — I want to thank the members of the Security Council for supporting today's resolutions," Bush said during the Security Council meeting.

During the 20-minute speech before the General Assembly, Bush urged the elimination of agricultural tariffs and other barriers that he said distort trade and stunt development. The goal, he said, is to open markets for farmers around the world.

"Today I broaden the challenge by making this pledge: The United States is ready to eliminate tariffs, subsidies and other barriers to free flow of goods and services as other nations do the same," Bush said.

"It's the key to overcoming poverty in the world's poorest nations. It's essential we promote prosperity and opportunity for all nations. By expanding trade we spread hope and opportunity to the corners of the world and we strike a blow against the terrorists who feed on anger and resentment."

Bush called on other nations to help the Group of Eight industrialized nations meet its pledge to rid the world of AIDS in the next generation. He also announced an initiative to fight avian flu. The International Partnership on Avian and Pandemic Influenza would require countries facing an outbreak of the virus to provide information and flu samples to the World Health Organization.

In a cozier setting Wednesday during a luncheon, Bush offered a toast to U.N. Secretery General Kofi Annan and noted the importance of this year's anniversary.

"Our ongoing efforts together will be crucial to enable the United Nations to fulfill the promises made 60 years ago," Bush said. "Mr. Secretary General, on this important anniversary, I offer a toast to you and to the United Nations. May the U.N. embody the high ideals of its founding in the years to come."

Adoption of a draft document regarding reforms for the world body is one of the top priorities for the United Nations. Late Tuesday, agreement was reached on a set of reforms that had been long sought by the United States, U.S. Undersecretary of State Nicholas Burns (search) said.

"This was an extraordinarily difficult process," Burns told reporters shortly after the declaration was completed on Tuesday afternoon, just in time for the annual event. "This is not the end of the reform effort, it really is the beginning of a permanent reform effort that must be under way at the United Nations."

The United States compromised on some elements of the reform package, originally put forth earlier this year by General Assembly President Jean Ping. U.S. ambassador to the United Nations John Bolton (search) had put together his own list of changes — about 750 of them to the 39-page document — drawing criticism from some U.N. watchers but also drawing praise from some international delegations for moving the process along.

Among the reforms, the package:

— establishes a Human Rights Council to promote universal respect for human rights (the council will not have to be elected by a two-thirds majority in the General Assembly and doesn't bar known rights violators);

— supports an internal ethics office and asks that the internal U.N. watchdog, the Office of Internal Oversight Services, be strengthened "as a matter of urgency;"

— creates a peace-building commission to help nations emerge from war;

— seeks a comprehensive terrorism convention but doesn't call for a definition of terrorism that rules out attacks on civilians, as Secretary-General Kofi Annan (search) had wanted;

— promotes development and expresses support for wealthy countries to set aside 0.7 percent of gross national product for development aid;

— encourages protecting civilians from genocide but creates no obligations to intervene where genocide is said to be occurring.

Bolton on Tuesday expressed optimism over the negotiation process that accompanied the document's production.

“I think we are encouraged at the shape of what will be the outcome document,” Bolton said, noting progress on terrorism, human rights and management issues. “We are optimistic that, although it won’t be everything we sought, we will have a strong outcome document.”

With adoption nearly assured, Bush also discussed other items with other world leaders attending the session.

"We will, of course, discuss areas of interest like economic matters. We will discuss North Korea and Iran,” both of which pose a threat because of their apparent efforts to develop nuclear weapons, President Bush told Chinese President Hu Jintao Tuesday when the two met in New York. Bush is expected to deliver an address to the General Assembly during its world summit.

“We have a lot to discuss,” Bush said. After the meeting, the White House announced that Bush had accepted an invitation from President Hu to visit China. The president will head to that nation and the APEC summit in South Korea in November.

Earlier on Tuesday, Bush and Iraqi President Jalal Talabani spoke to reporters before the two men left to prepare for the U.N. meeting.

Bush said that the U.N. session will mark “the first time in a half century that Iraq is represented by a freely elected government."

While “there’s going to be difficult days ahead. … I have no doubt about the impact of a democratic Iraq on the rest of the world,” which Bush said would include helping to pacify the Middle East and making the United States and the world safer.

While making his annual address to the General Assembly, the president afterward held two high-level meetings with British Prime Minister Tony Blair and Israeli Prime Minister Ariel Sharon. On Friday, Bush is holding a one-on-one meeting with Russian President Vladimir Putin.

Fox News' Greg Kelly and The Associated Press contributed to this report.