U.N. Secretary-General Ban Ki-moon is appealing to world leaders to help end Syria's civil war.
Mr. Ban told heads of state at the opening of the U.N. General Assembly he looks forward to an "enforceable and binding" Security Council resolution on Syria's agreement to give up its chemical weapons.
U.S. President Barack Obama told the gathering such a resolution must include consequences if the Syrian government fails to keep its commitments under the U.S.-Russian deal.
Turkish President Abdullah Gul later said he hopes the deal will be a first step in ensuring the elimination of all weapons of mass destruction in the Middle East. But he said it is a "disgrace" the Security Council has failed to uphold its responsibility to the people being killed in Syria.
President Obama also said he is directing U.S. Secretary of State John Kerry to pursue a diplomatic agreement on Iran's nuclear program. Mr. Obama said he firmly believes "the diplomatic path must be tested."
French President Francois Hollande said he expects "concrete gestures" from Iran to show it will give up its military nuclear program.
Iranian President Hassan Rouhani is to address the group later in the day, after urging Western leaders Monday to engage Iran and ease painful economic sanctions against his country. Mr. Hollande is also expected to meet with the Iranian leader.
Mr. Obama said he believes the United States is "exceptional" in its willingness to stand up not only for its interests, but the interests of all. He stressed the United States is prepared to use all elements of its power, including military force, to secure its interests in the Middle East.
President Obama said the United States is also determined to resolve the Israeli-Palestinian conflict.
The U.S. leader spoke after Brazilian President Dilma Rousseff, who reiterated her nation's concerns about recent disclosures of U.S. cyber-spying in Brazil and other countries. Ms. Rousseff said it is a "breach of international law" and a serious violation of human rights and liberties. She called the U.S. claim it intercepted data to protect nations from terrorism "untenable."
The Brazilian leader called for an international framework to regulate the Internet.