(CNN) Up to 16,000 people have fled the violence in Syria's war-ravaged eastern Aleppo, with food stocks "practically finished" and every hospital bombed beyond use, the UN's humanitarian chief said Tuesday.

But nearly 200,000 people are believed to be still in eastern Aleppo, as the Syrian regime pounds it with airstrikes and troops storm through it in an operation to retake the enclave after more than four years of rebel control.

"I am extremely concerned about the fate of civilians as a result of the deeply alarming and chilling situation unfolding in Aleppo city," UN humanitarian chief Stephen O'Brien said in a statement.

"Initial reports indicate that up to 16,000 people have been displaced, many into uncertain and precarious situations. It is likely that thousands more will have no choice but to flee should fighting continue to spread and intensify over the coming days."

Government forces and armed paramilitary groups loyal to Syrian President Bashar al-Assad began a renewed push toward eastern Aleppo on November 15, as regime warplanes continued to pound the area to flush out rebels and civilians.

They have made rapid territorial gains since entering eastern Aleppo on the ground Saturday , taking a huge portion of the northeast. Russian media on Monday cited its defense ministry, saying 40% of the east was now in regime hands, however CNN sources put the figure at just over 20%. Their gains drive a wedge through the zone and splits it into two sections.

"There are no modes of transportation and no vehicles in the streets, so civilians are fleeing and walking close to 8 or 9 kilometers on foot, carrying what they can and their children, and fleeing towards the western parts of Aleppo," an activist told CNN.

Rescuers debilitated

Hospitals have been obliterated in months of bombing and by the start of this week there wasn't a single one in operation, O'Brien and medical organizations have said.

Russian President Vladimir Putin ordered mobile field hospitals be sent to Aleppo to provide immediate medical assistance to residents, Kremlin spokesman Dmitry Peskov told the state-run Sputnik news network on Tuesday.

Russia has been the Syrian regime's closest and most powerful ally, and its support has been widely blamed for the destruction of hospitals and schools across the country in aerial bombardments.

Russia will send a multipurpose hospital to serve 100 patients, which includes a children's ward, as well as a mobile field hospital for 50 patients, which can also provide ambulatory treatment for some 200 people per day, Peskov said.

A Syrian girl after airstrikes hit the al-Shear neighborhood in Aleppo on Monday.

More than 500 people were killed between Saturday and Monday in the latest assaults, the self-styled Syria Civil Defense, a volunteer rescue group also known as the White Helmets, told CNN.

An additional 25 were killed overnight as the regime dropped parachute bombs in the Bab al-Nayreb neighborhood, an activist from the Aleppo Media Center said, adding dozens more had been injured.

Residents in several other areas under heavy bombardment Tuesday told CNN that the ambulances and rescuers that usually come after the strikes were nowhere to be seen.

"Unfortunately, we can't do our duty due to the lack of fuel," White Helmets member Bebars Meshaal told CNN.

Among those affected in the days of strikes is 7-year-old Bana Alabed, who has captured international attention with her tweets about daily life in eastern Aleppo. On Tuesday she shared a picture of her damaged home, posting that she felt "sad but happy to be alive," following a flurry of tweets in recent days recording heavy bombardment on her house.

This is our house, My beloved dolls died in the bombing of our house. I am very sad but happy to be alive.- Bana pic.twitter.com/9i0xxJrQtD — Bana Alabed (@AlabedBana) November 29, 2016

Before the evacuations in recent days, UNICEF said there were around 100,000 children in eastern Aleppo.

'Restore basic humanity'

Eastern Aleppo has become the epicenter of Syria's civil war, much of it decimated in regime strikes backed by Russian air power.

Assad has vowed to take the whole of Aleppo, which has for years been divided between the largely regime-held west and rebel-held east.

The government has besieged the east a number of times, cutting off both the rebels and civilians from the outside world, leaving communities on the brink of starvation -- without sufficient food, clean water, fuel and medical supplies.

A pro-government soldier looks over the city of Aleppo on Monday.

The last UN rations in Aleppo were distributed on November 13, and UN humanitarian adviser Jan Egeland warned last week that people in the area were on the brink of starvation.

"I ask all parties to the conflict to restore basic humanity in Syria," the UN's O'Brien said, calling for an end to the siege and for the safe passage of aid deliveries into the area.

Beginning of the end?

Taking all of Aleppo would mark a turning point in the Syrian war -- the city is the last urban rebel stronghold in the country. Seizing it would put the regime back in control of all four major cities.

Some observers have suggested it would be the beginning of the end of the uprising that began in 2011.

A solution to the war, which has drawn in both Russia and the US, has evaded the international community for years. Russia has used its veto power in the UN Security Council several times to shoot down proposed resolutions on the conflict.

French Foreign Minister Jean-Marc Ayrault called on the Security Council to immediately meet and examine the situation.

"More than ever, there is an urgent need for a cessation of hostilities and unhindered access to humanitarian assistance," Ayrault said in a statement, adding he would meet with the head of Aleppo's district councils, Brita Hagi Hasan, on Wednesday in Paris.

A man helps evacuate a wounded victim after airstrikes in al-Shear, Aleppo, on Monday.

O'Brien also called for a political solution, saying that "the people of Syria have suffered far too much and for far too long."

"More than anything, I hope a path towards a political solution can be found soon so that we can give some semblance of hope to the many millions of Syrian families who tonight are hungry, sick, and fearing for their lives," he said.