The resolution calls for stepped-up efforts to prevent the spread of nuclear weapons, promote disarmament and "reduce the risk of nuclear terrorism."
President Barack Obama gaveled the U.N.'s most powerful body to order with presidents and ministers from the 15 member nations -- -- the first American president to preside over a Security Council summit.
"The historic resolution we just adopted enshrines our shared commitment to a goal of a world without nuclear weapons," President Obama said. "And it brings Security Council agreement on a broad framework for action to reduce nuclear dangers as we work toward that goal."
Hear President Obama's remarks:
The resolution reaffirms the council's commitment "to seek a safer world for all and to create the conditions for a world without nuclear weapons," the Associated Press reported.
It does not specifically mention countries by name, such as North Korea and Iran, but reaffirms previous Security Council resolutions relating to their nuclear plans.
Iran says its nuclear ambitions are for peaceful energy purposes, but others fear it is developing weapons.
On Wednesday, the first day of the United Nations General Assembly, Iran's plans came under fire. The five permanent members of the U.N. Security Council, and Germany, toldIran to prepare a "serious response" by Oct. 1 to demands it halt its nuclear program, or risk the consequences.
French President Nicolas Sarkozy said Iranian leaders were "making a tragic mistake" if they thought the international community would not respond. British Prime Minister Gordon Brown warned Iran - and North Korea - that the world would be even tougher on proliferation. But the Chinese foreign ministry has said that increasing pressure on Iran would not be effective.
In his speech, Iranian President Mahmoud Ahmadinejad did not directly mention the nuclear issue, but spoke of countries that undermined the development of other nations under the pretext of preventing arms proliferation.
At talks with world powers next week about its nuclear program, Iran will also offer to purchase enriched uranium from the United States for medical purposes, Ahmadinejad told the Washington Post and Newsweek magazine.
"Why not just let them sit and talk and see what kind of capacity they can build? I think it is good thing to happen," Ahmadinejad said of Iran's readiness to allow its nuclear experts to meet with international scientists about the program.
Ahmadinejad said the new proposal would be presented by a senior Iranian diplomat when he meets counterparts from the United States, Russia, China, Britain, France and Germany in Geneva on Oct. 1.
Iran has not previously allowed such a meeting and it would mark a historic first.
Also Thursday, the United States rejoined a biannual conference designed to win support for the treaty banning all nuclear bomb tests. The session brought together foreign ministers and other envoys from more than 100 nations that have ratified or at least signed the 1996 treaty. A speech by Secretary of State Hillary Clinton scheduled for later Thursday represented the first U.S. participation since 1999.
---- Compiled from wire reports and other media sources