Syrian government and allied forces advanced north of Aleppo, pressing their week-old offensive to take the insurgent-held, eastern part of the city after dozens of overnight air strikes.
The Syrian army told rebels to leave the area, offering safe passage and aid supplies.
The Syrian military, supported by Iranian-backed militias and Russian air power, began their push to take the whole of the divided city after a ceasefire collapsed last month. The assault has nearly destroyed eastern Aleppo's healthcare system, the U.N said.
An air campaign by the Syrian government and its allies was reinforced by a ground offensive targeting the besieged eastern half of the city where insurgents have been holding out.
The Syrian Observatory for Human Rights and the Syrian military said the army and its allies had advanced south from the Handarat refugee camp north of Aleppo city, which they took earlier this week, taking the Kindi hospital and parts of the Shuqaif industrial area.
Air strikes and shelling continued on Sunday, the Observatory said.
Zakaria Malahifji, of the Aleppo-based rebel group Fastaqim, told Reuters there were clashes in this area on Sunday.
The Observatory added that there was fierce fighting between rebels and government forces all along the front line which cuts the city in two.
The Syrian army said on Sunday that rebel fighters should vacate east Aleppo and it would guarantee them safe passage and necessary aid.
"The army high command calls all armed fighters in the eastern neighborhood of Aleppo to leave these neighborhoods and let civilian residents live their normal lives," the statement carried by state news agency SANA said.
HOSPITALS DAMAGED
The relentless Russian and Syrian air campaign in east Aleppo has damaged hospitals and water supplies.
East Aleppo came under siege in early July after its main supply route, the Castello Road, fell under government control.
Internationally brokered attempts to establish ceasefires to allow in United Nations humanitarian aid have failed, although other international and local aid groups have brought in limited supplies.
The U.N's Under-Secretary-General for Humanitarian Affairs, Stephen O'Brien, said he was "deeply alarmed by the ferocious pummeling of eastern Aleppo" and reiterated U.N. calls for a pause in fighting, medical evacuations and access for aid.
"The health system is on the verge of total collapse with patients being turned away and no medicines available to treat even the most common ailments."
"With clean water and food in very short supply, the number of people requiring urgent medical evacuations is likely to rise dramatically in the coming days," he said.
On Saturday, the largest trauma and intensive care center in eastern Aleppo was badly damaged by air strikes and had to close. Two patients were killed.
The Syrian American Medical Society (SAMS), which partly supported the hospital, said the hospital had been hit seven times since July, with three attacks this week alone.
"The situation in Aleppo is beyond dire … People are stuck under the rubble and we can't get to them because of the intensity of the shelling. We are pleading for help to stop the bombing," said Mohamed Abu Rajab, a SAMS nurse at the hospital.
SAMS said only five hospitals remained operational in east Aleppo.
The Syrian Foreign Ministry said in a statement carried by state media that the participation of Russia's air force in the conflict now in its sixth year had "tightened the noose on terrorist groups and reduced their ability to spread terror to other countries".
The Syrian government refers to all groups fighting against it as terrorists.
