"In addition to the existing corridors, we are organizing four more humanitarian corridors," head of the Russian reconciliation center in Syria, Lt.-Gen. Sergey Chvarkov said, according to the state-run Sputnik news agency.
Syria and Russia, its key military backer, announced the creation of the three initial corridors on Thursday, after Syrian forces encircled the city and cut off rebel supply lines.
Both governments say the corridors are to allow for the distribution of badly needed food and medical aid to civilians, who have been facing a humanitarian disaster in the devastated city, and to provide residents -- along with rebels who choose to surrender -- the opportunity to leave.
The Syrian government has declared a general amnesty for rebels who surrender to government authorities within three months. The government dropped leaflets over the city last week with instructions for residents on where to find the corridors and how to approach them.
Families begin to leave, say Syria, Russia
Dozens of families began trickling out of the rebel-held neighborhoods in the east of the city
on Saturday, Syrian state news agency SANA reported. They crossed into the government-controlled Salahaddin district, where Syrian army units sent them to makeshift shelters.
Sputnik quoted Chvarkov as saying the existing corridors have allowed 169 civilians and 69 militants who had laid down arms to flee.
Syrian state TV showed images of what it said were women and children leaving, along a street lined with damaged buildings.
However, two sources on the ground told CNN they had visited the crossings and seen no people using them, nor any sign that they had been opened.
Meanwhile on Sunday, Syrian rebels launched an offensive to break the Aleppo siege, a member of the political leadership of Ahrar al Sham said in a video statement posted online.
Ahrar al Sham
is an Islamist rebel group that is fighting Assad's army, ISIS and Kurdish forces.
Ahrar al Sham stated that all factions in the Islamist umbrella group Jaish al Fatah would take part in the battle across the 20 kilometer front line.
Witnesses told CNN they have seen an increase in artillery fire and rocket activity near the front lines. Many residents started fires hoping the smoke would obscure the vision of pilots flying overhead, witnesses on the ground said.
Aleppo, Syria's largest city before the war broke out in 2011 and the country's economic hub, has been a major battleground in the conflict, with rebel groups holding neighborhoods in the east of the city for years. They include so-called moderate factions such as the Free Syrian Army, as well as various Islamist groups, including those, such as Jabhat al-Nusra, that have been designated terrorist organizations.
Residents describe life under siege
The United Nations has warned of a potential humanitarian catastrophe in Aleppo as regime troops, backed by Russian air power, tighten their grip on the ruined city. An estimated 200,000 to 300,000 people remain in the besieged rebel-held part of eastern Aleppo.
In addition to the continual bombardment they face, which has seen numerous hospitals struck, residents complain of acute shortages of food, water and medicine.
"Markets are empty of vegetables and all other food products, streets are empty of cars and vehicles because there is no fuel," an aid organization manager based in Aleppo told CNN Sunday, as bombs continued to pound rebel-held neighborhoods.
He said the shortages had forced his organization to resort to reusing "single-use" medical equipment after attempting to sterilize it.
An emergency responder in Aleppo confirmed to CNN that rebel-held neighborhoods were under aerial bombardment from Russian jets Sunday. Ambulances and other emergency vehicles in the city were out of fuel, he said.
The United Nations' special envoy for Syria, Staffan de Mistura, has said that food supplies in rebel-held areas could run out within weeks.
Russia: Aid is ready for fleeing residents
Russia says that it has prepared 14 tons of humanitarian cargo for those who leave the city, with 2.5 tons of food and other essentials already supplied.
But some residents contacted by CNN say they are wary of the government's promise they will be safe if they leave the rebel-held areas.
The corridors also have been regarded with skepticism by international actors.
U.S. Secretary of State John Kerry suggested Friday that the corridor approach could potentially be a "ruse," telling reporters that it carried "the risk, if it is a ruse, of completely breaking apart the level of cooperation" between the United States and Russia.
However, he said, "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."
De Mistura says introducing such measures should be left to the U.N. and its partners, and has stressed that no one should be forced to leave.
And Amnesty International has questioned whether the corridors will help prevent a humanitarian disaster, saying many residents are unlikely to trust government assurances over their safety.
U.S.-backed force recaptures 40% of city of Manbij
Elsewhere in Syria, thousands of civilians have also fled ISIS-held parts of the northern city of Manbij, some 80 kilometers (50 miles) northeast of Aleppo, over the past day, the UK-based Syrian Observatory for Human Rights reported Sunday.
Backed by the air power of the U.S.-led coalition, the alliance of U.S.-backed Kurdish and Arab forces -- known as the Syrian Democratic Forces -- has been engaged in fierce clashes with the Sunni terror group in the city.
The SDF had recaptured about 40% of the city from ISIS as of Sunday, the UK-based monitoring group reported.
U.S. officials describe Manbij as a strategic supply point for ISIS, and the terror group's principal hub between Raqqa, the capital of its self-declared caliphate, and Turkey.
Clashes are still ongoing with ISIS militants in several other parts of the city, the observatory said.
More than 280,000 Syrians have been killed since fighting began in 2011, and millions have been forced to flee the country.