Clinton: World may not succeed in Syria NEW: Hillary Clinton praises a new international deal even as she admits it might fail NEW: She says there is "no way" President Bashar al-Assad could be part Geneva, Switzerland (CNN) -- There is no guarantee that a sweeping new international agreement on Syria will succeed in ending the conflict there, U.S. Secretary of State Hillary Clinton conceded, as opposition activists said the number of dead had skyrocketed in recent months. There is no guarantee that we are going to be successful. I just hate to say that," Clinton told CNN. But she expressed optimism that a new agreement hammered out Saturday would help ease President Bashar al-Assad out of power. The first plan backed by Russia and China as well as the West, it calls for a transitional government as a step towards ending the 16-month uprising. Opposition activists immediately criticized the deal as leaving open the possibility that al-Assad would remain in power. "The new agreement provides vague language which is open to interpretation," the opposition Local Coordination Committees of Syria said in a statement Sunday. But Clinton said al-Assad and his inner circle would be excluded from any transitional government. 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 20 people dying on Sunday, according to the opposition Local Coordination Committees of Syria. They 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. "Dr. Jamal Tabarneen was martyred by the regime's army gunfire while he was helping in resuscitating the injured in Zamalka's explosion," the LCC said. The international group meeting in Switzerland agreed that both the regime and opposition fighters should immediately adopt a cease-fire and implement Annan's six-point peace plan without waiting for the actions of others, Annan said. The group also called for a transitional government. Annan said it could include members of the current Syrian regime, making it theoretically possible that al-Assad will be a part of the transition. But Annan pointed out it is the Syrians who will decide the make-up. The LCC said it was "gravely concerned" by what could happen in a transitional period with al-Assad's military and security forces. CNN's Saad Abedine and Holly Yan contributed to this report.