The Syrian ambassador to the United Nations again blamed the violence on armed perpetrators that he claimed were supported and financed by Turkey, Saudi Arabia, Qatar and other nations.
"We are still committed toward guaranteeing the maximum success to the mission of Kofi Annan," Bashar Jaafari said at a news conference Tuesday. "But the Syrian government cannot do all the job alone."
He said the international community is hypocritical by not acting against terrorists in Syria as they do against al Qaeda.
Rice said no one could say with certainty that there are no foreign fighters in Syria. But she said that's not the key issue.
"This is substantially a diversion from the main point," Rice said. "The main point is that the government of Syria continues to kill its own people."
Many nations, including Syria's Arab neighbors, have condemned the ongoing violence, which has pitted a minority Alawite-dominated government against a predominantly Sunni uprising.
International leaders have said the Syrian government is targeting dissidents seeking democracy and the ouster of al-Assad, whose family has ruled Syria for 42 years.
The LCC says more than 11,000 people have been killed in 14 months.