BEIRUT - The U.N. Security Council unanimously approved a French-Russian deal on Monday to allow U.N. monitors in to oversee the evacuation of civilians and rebel fighters from the long-fought-over city of Aleppo in Syria.

CBS News’ Pamela Falk reports the resolution contains the proviso that interested parties, including Western-supported rebels and the Syrian government and their allies, must agree on the compromise resolution hammered out during hours of negotiations between France and Russia on Sunday. France had said the deal was necessary to avoid “mass atrocities,” in a war that has already seen as many as 500,000 deaths.

There are still hurdles for civilians trying to escape the massive bombing, but the vote illustrates compromise between Russia and France, as well as with the U.S. and U.K, over how to protect civilians in Syria as the government retakes areas held by the opposition.

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The U.N. resolution mandates that the evacuations must be conducted in accordance with international humanitarian law and says that the evacuations of civilians must be voluntary and to final destinations of the civilians’ choice. It also calls for protection to be provided to all those who choose or who have been forced to leave their homes.

U.S. Ambassador Samantha Power said before the resolution passed that “100 plus” U.N. personnel are ready to monitor evacuations once there is a green light. She said following the siege of eastern Aleppo, there have been “many, many reports of people being pulled off buses and disappeared, whether into conscription or into torture chambers or killed outright.”

The U.N. doesn’t know because it’s not there, Power said, but if monitors are deployed it could deter “some of the worst excesses.”

The fragile cease-fire between the rebels and the regime of Syrian President Bashar Assad resumed Monday morning, as buses resumed evacuating those still remaining in eastern Aleppo following days of delays, and others departed with the sick and wounded from two rebel-besieged Shiite villages in the country’s north.

The Britain-based Syrian Observatory for Human Rights and the pan-Arab Al-Mayadeen TV said that 10 buses left with civilians from the two Shiite villages long besieged by rebels — Foua and Kfarya — and were on their way to government-controlled areas on Monday. They reported that 15 additional buses entered the two villages to bring out more people.

According to the deal, more than 2,000 sick and wounded are supposed to leave the villages.

The evacuations from the villages were added on as conditions to a Turkey- and Russia-brokered cease-fire deal that paved way for the last rebels and civilians to leave the remainder of the rebel enclave in the eastern half of Aleppo.

The departure from the villages had stalled on Sunday after militants burned six empty buses assigned to take the villagers out.

The Observatory and Turkey’s Foreign Minister Mevlut Cavusoglu later said that since midnight Sunday, some 4,500 people have been evacuated from eastern Aleppo.

Reports differed on how many people remain in what was once the Aleppo rebel enclave, ranging from 15,000 to 40,000 civilians, along with an estimated 6,000 fighters.

Turkey’s state-run Anadolu Agency said a total of 131 wounded people — including 46 children — were brought to Turkey for treatment since the evacuations began last week. The agency said five of them have since died.

If the evacuation from Aleppo is completed later on Monday, it will close an important chapter in Syria’s civil war, now in its sixth year, with rebels having no remaining presence in Syria’s largest city, which was once the country’s commercial center.

The rebels captured eastern Aleppo in July 2012 and held on to it despite a ferocious assault in the past weeks by Syrian government forces, backed by Russia and a host of Shiite militias from Iraq, Lebanon, Iran and Afghanistan. The recapture of the entire city would be President Bashar Assad’s biggest victory since the Syrian conflict began in March 2011.