The families moved out of eastern Aleppo on Saturday through humanitarian corridors set up by the regional government, according to the Syrian state news agency SANA.
The civilians were "besieged by the terrorist groups in the eastern neighborhoods" and crossed into the Salahaddin section of the city, where Syrian army units sent them to makeshift shelters, the news agency reported. SANA also reported that several rebel gunmen surrendered.
Syrian state TV showed what it said were women and children leaving the city along a street lined with bomb-damaged buildings.
The Britain-based Syrian Observatory for Human Rights also reported that civilians were using a corridor in Salahaddin to enter government-controlled districts.
At least 169 civilians have left the city since Friday, the Russian state news agency Tass reported, and 69 militants have surrendered.
However, a journalist working for CNN visited the Salahaddin crossing after the initial government reports and saw no signs that it had opened.
The families are fleeing a city devastated by the relentless pounding by Russian and Syrian forces
, which are trying to retake swaths of the east that have been in rebel hands for nearly four years.
Plans for humanitarian corridors
Syrian and Russian officials on Thursday announced a plan to open three relief corridors to distribute food and medical aid to civilians, and provide them -- and rebels who chose to surrender -- the opportunity to leave the city.
Still, the creation of humanitarian corridors by Russia and Syria has been met with skepticism.
U.S. Secretary of State John Kerry told reporters Friday that the proposal "has the risk, if it is a ruse, of completely breaking apart the level of cooperation" between the United States and Russia.
"On the other hand, if we're able to work it out ... and have a complete understanding of what is happening and then agreement on the way forward, it could actually open up some possibilities," he said.
The United Nations special envoy for Syria, Staffan de Mistura, said the creation of humanitarian corridors should be left to the U.N. and its partners. "That's our job," he said.
He also pressed for guarantees on the protection of civilians and said no one should be forced to leave.
"Some civilians may want to avail themselves of the possibility afforded by the corridor and by the Russian initiative," he said. "When they do, it is crucial that they are given the option of living in areas of their own choice."
De Mistura warned that food supplies in Aleppo could run out within weeks.
"The clock is ticking," he said.
Matthew Rycroft, the UK ambassador to the United Nations, insisted that the humanitarian proposal be accompanied by an end to the bombing campaign.
"If the corridors could be used to allow aid into Aleppo, then that would be welcome," he said. "But clearly, the U.N. and the rest of us cannot be complicit in anything else -- for instance, any form of emptying of Aleppo, or preparing for an onslaught in Aleppo, or indeed any continuation of this medieval siege of Aleppo."
Too wary to leave?
Amnesty International has questioned whether the corridors would prevent a humanitarian catastrophe in the city, saying many civilians would likely be wary of government assurances and might not leave out of fear for their safety.
Philip Luther, director of Amnesty's Middle East and North Africa program, said the corridors were "not a substitute for allowing impartial humanitarian relief for civilians who remain in opposition-held areas of the city or other besieged areas, many of whom will be skeptical about government promises."
Many Aleppo neighborhoods have come under fire for 80 consecutive days, with more than 6,000 people -- mainly civilians -- killed or injured. Four hospitals have been hit
. Rebel fighters, striking back with artillery and bombings, have been unable to match the firepower of government forces backed by Russia.
Much of Aleppo, the country's largest city and a vital economic hub, has been reduced to an apocalyptic wasteland.
Between 200,000 and 300,000 people are believed to still reside in rebel-held Aleppo. Many are elderly people who are too sick or too stubborn to leave.
On Thursday, leaflets were dropped over the city with instructions on how to approach checkpoints and a map showing the corridors.
Those wanting to leave are supposed to wave the leaflet with their right hand raised above their head and the other hand either around their head or holding a child's hand, the leaflet said. Residents would also be notified by loudspeakers and text messages.
More than 280,000 Syrians have been killed since fighting began in 2011, with millions forced to flee the country.