A sixth straight day of assaults by government forces in the rebel-held east of the city has left the situation increasingly desperate, with reports the death toll is now around 240.
But the Syrian government has refused a proposal from the United Nations to grant eastern Aleppo autonomy as part of a solution to restore peace.
The latest onslaught in the city of Aleppo has been one of the most intense in Syria's almost six year-old civil war.
The violence is becoming increasingly palpable and widespread, with the latest fighting killing at least eight schoolchildren.
While the rebel-held eastern district has been the main subject of the ferocious campaign, the government-held west has now been shaken by a wave of brutality, too.
Syrian state television and the British-based Syrian Observatory for Human Rights say a rocket attack by rebel forces has killed the eight children at their school.
UN Special Envoy for Syria Staffan De Mistura says he has discussed the latest violence in a meeting with Syrian foreign minister Walid al Moallem.
"I also, frankly, expressed concern, which is fair to say, about mortar shelling which has been recently taking place here in Damascus and some victims, children actually, in west Aleppo as well."
The bombardment continues in east Aleppo, where, in the latest attack, a barrel bomb killed a family of six.
The Syrian Observatory for Human Rights says, since the government renewed its assault there last week, 240 people have been killed.
The World Health Organisation says all hospitals in the area have been knocked out.
This man, believed to be a doctor, has spoken of a direct hit to an intensive-care unit full of patients, many of them transfers from other bombed facilities.
"Our hospital has sustained severe material damage. There's a state of panic among patients and medical-staff members. Ambulance vehicles are stranded outside, and they can't help any patients."
With all hospitals in east Aleppo out of action, the quarter of a million people trapped there are without healthcare.
International Committee of the Red Cross spokesman Pawel Krzysiek has told CNN there is no way to deliver aid to the area.
"What we don't have is access to eastern Aleppo, the place where ... the besieged place, where approximately 250,000 people are in desperate need of humanitarian aid."
At the meeting in the Syrian capital Damascus, Mr De Mistura says he has expressed outrage to the Foreign Minister over hospitals allegedly becoming targets.
"I started, frankly, by expressing serious concern and, indeed, shared the general international outrage for the news coming from eastern Aleppo, as reported by WHO and others, of several hospitals being heavily bombed by aerial bombs."
But he says Mr Moallem denied any bombing of hospitals.
"It is fair to say that Minister Moallem denied that any bombing of eastern Aleppo hospitals had taken place."
Mr De Mistura proposed east Aleppo be given autonomous administration as part of an approach to restore peace there.
But Mr Moallem refused, saying the move would be a violation of Syrian sovereignty.
Aleppo has been split since 2012, with the east under sustained bombardment by government forces, backed by Russia, targeting what they say are terrorist groups.
Mr Moallem says, once they have been expelled, the state's institutions must be restored.
"We agree on the need that terrorists must leave eastern Aleppo, but it is not acceptable that some 275,000 of our citizens be left to be hostages to 6, 5 or 7,000 gunmen. There is no government in the world that would accept that."
