The deal would send United Nations monitors to observe the evacuation process after consultations with “interested parties,” which means that observers could in theory be turned down by soldiers and militias on the ground. Senior United Nations officials have repeatedly said that they have sought Syrian government permission to be present during the evacuation process, and that they have not received it.
“This would give us collectively the tools to avoid another Srebrenica,” said François Delattre, the French ambassador, referring to the massacre of civilians in that besieged city in Bosnia in the Balkans war over 20 years ago.
The measure demands that the warring parties “provide these monitors with safe, immediate and unimpeded access.”
Samantha Power, the United States ambassador to the United Nations, said she expected the resolution to be approved unanimously. She said she hoped monitors would be sent immediately to accompany civilians who want to leave on buses, and to monitor their treatment at checkpoints.
Earlier in the day, before walking into negotiations, Vitaly I. Churkin, the Russian ambassador, had said United Nations staff members should not be told to “go wander around the ruins of Aleppo without proper preparation.” Mr. Churkin told reporters on the way into the Security Council chambers: “It has disaster written all over it. This is a provocation.” He declined to answer questions after the consultations had wrapped up.
There are hundreds of United Nations civilian staff members stationed in government-held cities in Syria who could be deployed as monitors, the United Nations said. At the moment, only monitors from the International Committee of the Red Cross and their local partners with the Syrian Arab Red Crescent are on the ground. They do not report to the Security Council.
The United Nations did not help broker the evacuation agreement, but its officials have been pleading for access to the process to investigate reports of atrocities, which have included suspected killings by pro-government forces of scores of people in eastern Aleppo.
The United Nations secretary general, Ban Ki-moon, last week described the area, which has been besieged for months and heavily bombarded by Syrian forces, as “a synonym for hell.”
Last week, the United Nations’ top envoy to Syria, Staffan de Mistura, said that he had repeatedly asked the Syrian government for permission to allow United Nations staff members to witness the evacuation of civilians and fighters — but that no permission had been received.
On Sunday, his humanitarian adviser, Jan Egeland, repeated that call. “It is important that there are third parties present to witness and assist,” Mr. Egeland wrote in an email.
Carrying out the evacuations requires the cooperation not just of foreign powers but also of the loose coalitions of fighters in Syria. Fighting for President Bashar al-Assad are Syrian soldiers, the Hezbollah militant group from Lebanon, and other Shiite militias from Iraq and elsewhere. They receive support from Iran and Russia, which has been launching airstrikes on insurgent communities.
On the other side is a patchwork of Sunni rebel militias, including some extremists, who have received support from the United States, Turkey and Persian Gulf countries like Saudi Arabia and Qatar.
Nearly six years into the war, both sides have resorted to siege tactics, surrounding communities populated by their foes and bombarding them.
The evacuation of eastern Aleppo was to begin on Wednesday, but it was aborted after gunfire on the route. Convoys of ambulances and buses began on Thursday to bring about 3,000 civilians and fighters out of eastern Aleppo.
At the same time, another convoy headed for two Shiite villages in Idlib Province, Fua and Kfraya, that are surrounded by Sunni rebels, but their way was blocked. By Friday morning, the evacuations had stopped.
They resumed on Sunday. Syrian state television reported that one convoy had reached eastern Aleppo, where thousands of people are waiting to be evacuated. But rebel gunmen attacked the convoy heading to the Shiite villages, setting a number of the buses on fire.
Late Sunday night, Robert Mardini of the International Committee of the Red Cross said on Twitter that evacuations had resumed.
Videos posted online showed gunmen near the buses shouting “God is great” and using derogatory terms for Shiites.
After the buses heading to the Shiite villages were burned, and a driver killed, according to Mr. Egeland, pro-government forces prevented buses from leaving eastern Aleppo, according to residents reached inside the neighborhood.
A resident of eastern Aleppo reached by phone said that he had been waiting for hours on a packed bus to leave the neighborhood, but that the government checkpoint would not let them pass.
“This is the third time I have tried to leave,” said the resident, who gave only his first name, Saleh, for safety reasons. “There is a sense of fear among the people here.”