United Nations Secretary-General Ban Ki-moon opened the annual General Assembly summit by appealing to world leaders to stop sending weapons to Syria.
Ban appealed to "all states to stop fueling the bloodshed and to end the arms flows to all parties."
In his address to world leaders, U.S. President Barack Obama discussed the need for a strong response to chemical weapons use in Syria.
Obama speaks hours before Iranian President Hassan Rouhani, who urged Western leaders Monday to engage Iran and ease painful economic sanctions against his country.
Those sanctions stem from concerns that Iran is seeking to develop nuclear weapons and its repeated refusal to heed U.N. demands to suspend its uranium enrichment. Iran insists its nuclear program is solely for peaceful purposes.
U.S. officials say there is no meeting scheduled between Obama and Rouhani while they are in New York, but have not ruled out the possibility. U.S. and Iranian government heads have not met since before the 1979 Islamic revolution that toppled the U.S.-backed Shah.
A group of top U.S. senators called on Obama to reiterate in his speech that the U.S. will not accept a nuclear-capable Iran, and that the sanctions will continue despite Rouhani's overtures.