"We want the U.S. to step forward and take the leadership right now to push for Assad to step down and allow for a transitional government from the opposition."
Emphasizing that the opposition has not asked for "boots on the ground," Atassi said U.S. military action should remain "on the table." And, she said, the rebels are looking to Washington for help empowering moderate elements of the opposition.
"We are not terrorists," she said.
Militant groups make up part of the Syrian opposition.
In his remarks to open the General Assembly on Tuesday, U.N. Secretary-General Ban Ki-moon called for the Syrian government to "fully and quickly" honor its obligations under the Chemical Weapons Convention, which calls for turning over control of its stockpiles.
Ban also appealed to all sides to stop supplying any weapons to all parties in the Syrian civil war while urging both the Syrian government and the opposition to respect international humanitarian law.
Russia and Iran, as well as Hezbollah in Lebanon, are providing military backing to the al-Assad regime while the United States and some European allies have started supplying light arms to rebel fighters.
Meanwhile, U.N. weapons inspectors will be back in Syria on Wednesday to assess at least six claims of chemical weapons use in Syria by the regime or rebels, a spokesman for Ban said Tuesday.
Al-Assad hinted at potential trouble for inspectors coming into Syria, saying other countries may order terrorists to attack them.
"Those militants might want to stop (the) experts' arrival. We know that those terrorists are under the control of some countries," he said in an interview Sunday with Chinese television. "And those countries may encourage the terrorists to stop experts from arrival, so that they could accuse the Syrian government for violating the agreement."
Despite al-Assad's veiled threat, positive progress has been made on the Syrian chemical weapons deal brokered by the United States and Russia in Geneva. Over the weekend, the United States said it was pleasantly surprised by the extent of Syria's initial declaration of its chemical weapons stockpile reported to the Organisation for the Prohibition of Chemical Weapons.
The United States is pushing for a U.N. Security Council resolution this week in New York to enforce the Geneva deal.
Brazil outrage over U.S. surveillance
Obama faced criticism Tuesday from Brazilian President Dilma Rousseff, who used her U.N. speech to call allegations of U.S. surveillance of her country "totally unacceptable."
Rousseff referred to classified leaks by former National Security Agency contractor Edward Snowden that made public how the U.S. government had access to phone and Internet records, including foreign information.
She said the U.S. surveillance intercepted private details of Brazilian citizens and businesses, along with "communications by Brazilian diplomatic representation offices, including the permanent mission of Brazil with the United Nations and even the very presidency of the republic of Brazil."
"Meddling in such a manner in the life and affairs of other countries is a breach of international law and such is an affrontment to the principles that should otherwise govern relations among countries, especially among friendly nations," she said, adding Brazil would propose U.N. action intended to prevent the manipulation of cyberspace as "a weapon of war."
Because of the surveillance controversy, Rousseff postponed a state visit to Washington that had been planned for next month. The White House said the postponement was a joint decision.