Both sides have to agree on the membership of the interim body, and Clinton said there was "no way anyone in the opposition would ever consent to Assad or his inside regime cronies with blood on their hands being on any transitional governing body."
"Assad will not be part of it," she said in an interview late Saturday in Geneva, Switzerland, after the deal was hammered out.
Kofi Annan, the joint special envoy for the United Nations and Arab League, invited diplomats from the U.N. Security Council and envoys from Turkey, the United Nations, the European Union and the Arab League to the global meeting in Geneva on Saturday.
Clinton said the Russians, who have long been al-Assad's most steadfast supporters, had finally decided to back a transition away from his rule.
"They have committed to trying," she said. "But they also admitted that they may or may not have enough leverage to convince not just one man, but a family and a regime that their time is over."
Bloodshed continued unabated in the wake of the international talks, with at least 69 people dying on Sunday, according to the opposition Local Coordination Committees of Syria.
It said Sunday that more than half of the people killed since the Syrian crisis began 16 months ago were slaughtered in the past four months.
More than 14,000 people have been killed by the regime, according to tallies from opposition activists.
June was a particularly gruesome month, with 2,386 people killed compared to 1,196 in May, the LCC said.
The dead on Sunday include several people who died from injuries sustained in a blast at a funeral procession in Zamalka on Saturday, the group said.