"The Security (Council) must explicitly require this of all participants," al-Jabar said.
He said the 15-nation council should impose targeted sanctions against Damascus if it rejects a transition.
Al-Jabar said he would take part in peace talks in Geneva if Damascus "explicitly" would transfer all authority to the transitional body. A conference last year in Geneva called for a political and democratic transition to end the conflict, which arose after a bloody regime crackdown on pro-reform demonstrations in early 2011.
"The situation in Syria is desperate," al-Jabar said. "The Syrian people are calling for peace and democracy. We need more international pressure to force the Assad regime to accept a transition regime."
Diplomats who met with al-Jabar and his delegation said the discussion covered issues from human rights to prospects of a political settlement.
"We received a positive message and a strong commitment to unity and democracy in Syria," British Ambassador Mark Lyall Grant said following a three-hour meeting. "They rejected extremism and terrorism."
French Ambassador Gerard Araud said the Syrian opposition gave a "clear commitment" to a new Geneva conference while demanding that Damascus relinquish power to the transition government.
Russian Ambassador Vitaly Churkin, whose country backs al-Assad, called the meeting "useful."
"We should not be carried away (by the commitment). The meeting was not to officially recognize the coalition," he cautioned.
UN Secretary General Ban Ki-moon called Thursday for every effort to be made to halt the Syrian civil war: "The conflict has killed more than 100,000 people and displaced millions of people, and we have to bring it to an end."
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