The resolution makes no mention of whether or not Mr. Assad would be able to run for office in new elections, which the resolution says must be held in the next 18 months.
There are still gaps to be reconciled between the American and Russian positions, but the agreement has enabled the Security Council to give its imprimatur to a possible political solution for the first time since the civil war started nearly five years ago.
One possible obstacle to implementing a deal will be determining which of the disparate rebel groups would participate in the talks scheduled to begin next month, and whether they would agree to come to the table at all without a guarantee of Mr. Assad’s exit.
The resolution also leaves open the question whether other rebel groups can be designated as terrorist organizations and would fall outside the cease-fire agreement. The resolution embraces an effort led by Jordan to develop “a common understanding” for determining which groups are terrorist and which can participate in political talks with the Syrian government, allowing the fight against the Islamic State militants and the Qaeda-affiliated Al Nusra Front to continue.
The resolution endorses a process begun by Secretary of State John Kerry to bring together the Russians, Iranians, Saudis and other major regional players with European governments to develop a diplomatic road map for resolving the Syrian conflict.
Diplomats from more than a dozen countries met at the Palace Hotel in New York on Friday to discuss a possible resolution.
At issue was whether the countries that all have stakes in the outcome of the war can end the fighting, and by doing so, help stem the refugee crisis in Europe and the threat posed by the Islamic State.
The last two rounds of talks, held in Vienna in October and November, produced a diplomatic road map for Syria: a cease-fire by January; talks between the Syrian government and opposition parties, mediated by the United Nations; and elections in 18 months.
The draft of the resolution agreed Friday by the so-called International Syria Support Group appears to include these three steps. The group is led by the envoys of the United States and Russia, and includes the regional rivals Iran, Saudi Arabia and Turkey — which have vastly different agendas in Syria. The Arab League and the European Union also participated.
American officials said that before the full group began its discussions on Friday, Mr. Kerry had conferred with his Russian counterpart, Sergey V. Lavrov, and that they had then met with envoys of the other three permanent members of the Security Council — Britain, China and France.
Western diplomats at the United Nations said they were not certain a consensus could be reached. “There are still differences of opinion about Assad and his specific future,” John Kirby, a State Department spokesman, told reporters in Washington on Thursday.
Mr. Kirby referred to the agreement struck at the last meeting of the support group, which left Mr. Assad’s future unresolved. It called for “a unified, pluralistic, nonsectarian, whole Syria,” he said.
One of the trickiest parts of the road map for diplomacy was expected to be composing the list of groups in Syria that are considered terrorist organizations and would be excluded from the peace process.
The emerging agreement on Friday comes after a rare show of unity among the world powers Thursday afternoon, when the Security Council unanimously adopted a legally binding resolution intended to prevent the Islamic State, Al Qaeda and other terrorist groups from raising money.
One of the most incongruous parts of the resolution was that the government of Syria was one of its co-sponsors.
The Syrian ambassador to the United Nations, Bashar al-Jaafari, told reporters on Thursday that he would participate in the Council meeting on Friday.
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By SOMINI SENGUPTAand DAVID E. SANGER http://www.nytimes.com/2015/12/19/world/middleeast/syria-talks-isis.html?emc=edit_na_20151218&nlid=58310307&ref=headline&_r=0