Pakistani President Musharraf seemed to capture the mood during the first week. He said it was essential to resolve issues such as the development gap between rich and poor states and disputes affecting Muslims. He warned that what he called an "iron curtain" could descend between the West and the Islamic world.
"The time for closing fronts has come," Musharraf said. "The world today is crying for peace, reconciliation, and reform. Our objective today has to be harmony through reconciliation and accommodation globally and regionally."
Many representatives seized on Security Council reform as the key route for achieving progress on such matters.
With 191 states, the UN now has nearly four times more members than it did at its founding 59 years ago. Yet the Security Council has changed membership just once, from its 11 original members to 15. Most control resides in the five veto-holding states -- known as the P-5 -- who reflect the world's power structure at the end of World War II.
There is near-universal agreement that the Security Council should be expanded. But differences over adding permanent or nonpermanent seats have divided the General Assembly for 10 years.
Proponents of expanding permanent membership say this year's debate shows there is momentum in their favor. Foreign ministers of Brazil, Germany, India, and Japan met on the sidelines of the assembly to affirm their plan to seek permanent membership.
A diplomat from one of these states told RFE/RL he believes they will have the backing of two-thirds of the assembly as required by the UN Charter when the restructuring issue is voted on as expected in 2005.
There is no expectation that the veto power assigned the original permanent five will change.
The diplomat said: "We can't demolish the privileges of the P-5, but we can tackle them."
UN Secretary-General Annan has tasked a high-level panel to recommend a series of institutional changes, such as council reform, to help meet this century's security challenges. The panel will report by December.
Annan opened the debate by noting the shortcomings in the current body of international law. But, citing abuses from Iraq to Sudan, he said states were willfully violating existing laws.
"Today, the rule of law is at risk around the world," Annan said. "Again and again, we see laws shamelessly disregarded -- those that ordain respect for innocent life, for civilians, for the vulnerable, especially children."
A number of small states, noting Annan's warning, expressed concern about the use of unilateral military force, as in Iraq.
For many larger states, mounting effective efforts against terrorism was a chief concern. Among them was Russia, whose Foreign Minister Sergei Lavrov focused his address almost entirely on terrorism in the wake of the Beslan attacks. Lavrov suggested a need to reshape global legal norms to help confront new threats.
"International law is clearly not an inalterable dogma," Lavrov said. "The fight against terrorism calls for its development and improvement."
During the assembly meeting, Russia circulated a draft resolution calling for an expansion of the UN blacklist of individuals, groups, and entities involved in terrorism. They would face an assets freeze, an arms embargo, and "expedited extradition." The measure met with immediate support from the United States and Britain, but it is unclear when the council will act on it.
U.S. President Bush defended the U.S. decision to invade Iraq, saying it was necessary for the Security Council to uphold its resolutions. Bush emphasized the importance of maintaining support for democracy-building in Iraq and Afghanistan.
He hit on theme that has come to dominate his presidential reelection campaign -- that spreading democracy throughout the Middle East will strengthen global security.
"For too long many nations, even my own, tolerated -- even excused -- oppression in the Middle East in the name of stability," Bush said. "Oppression became common, but stability never arrived."
Bush announced a proposal for a democracy fund within the United Nations to build the capacity for democratic governance in states in transition. U.S. officials acknowledge that the UN Development Program already runs democracy projects, but they say a distinct fund will help better focus on reforms such as setting up independent courts, a free press, political parties, and trade unions.
U.S. officials said the fund was welcomed by many members of the Community of Democracies, which held a ministerial meeting on the sidelines of the assembly debate.
Bulgarian Foreign Minister Solomon Pasi told RFE/RL after the meeting that the fund was a good idea.
"Of course we cannot sponsor democracy without the necessary mechanisms, without the leverages -- and creating a fund of this type is certainly a mechanism which helps," Pasi said.
The group issued a communique pledging to strengthen regional cooperation for democracy. But it stopped short of creating a permanent structure that would hold regular meetings at the UN, as requested by nongovernmental human rights groups.
The General Assembly president, Foreign Minister Jean Ping of Gabon, told reporters that democratic reforms were one of the most talked-about issues at the session. But he noted the comments of one government representative who warned against what he called an "instant coffee"-type approach to spreading democracy:
"He said that what counts in democracy is values, not mechanism," Ping said. "It is values, which means that [it will work] provided that it is coffee, and real coffee, and which suits the tastes of the people. There is nothing which is standard or pret-a-porter."
U.S. and European officials hope a new stress on democracy will help reform bodies like the UN Human Rights Commission. Rights groups say the commission's work is regularly undermined by the membership of countries such as Cuba and Sudan.