Syrian rebels and pro-government forces have clashed on several fronts around Aleppo as the country's military command called on militants to evacuate the city.
The UK-based Syrian Observatory for Human Rights monitoring group reported fighting in areas close to al-Shuqeef hill and the Bustan al-Basha area as the government tries to penetrate the city's opposition-held eastern side.
The reports come a day after pro-government forces captured the al-Shuqeef hill.
The government's offensive has been accompanied by a relentless Russian and government campaign of air strikes across eastern Aleppo.
President Bashar Assad's forces are depending on Russian air strikes and Iran-backed militias to bolster their campaign.
A spokesman for the Nour el-Din el-Zinki rebel faction told The Associated Press that foreign fighters were actively participating in the government's ground campaign for the city. He said rebels could identify Lebanese and Iraqi militias by their flags.
An air strike, meanwhile, targeted a rebel headquarters near the central city of Hama on Sunday, killing at least six militants, the Observatory said.
The blow is a setback for the rebel campaign to advance on the government-controlled city.
The UN's humanitarian chief Stephen O'Brien said on Sunday that east Aleppo's health system has been "all but obliterated" by shelling and bombardment.
"Medical facilities are being hit one by one," Mr O'Brien said in a statement that called for at least a weekly 48-hour humanitarian pause to the fighting.
The UN estimates 275,000 people are trapped in the east by a government siege.
"We are in a race against time to protect and save civilians in eastern Aleppo city. They need our urgent action to bring an end to their living hell," Mr O'Brien said.
Air strikes put one of the city's largest hospitals, located in the eastern Sakhour area, out of service on Saturday, doctors and activists reported.
The Syrian military command said in a statement carried on state news on Sunday that government forces would guarantee the gunmen safe passage out of the city's opposition-held eastern areas.
Russia, which backs Mr Assad's government, announced a month ago that the government would open safe passages for civilians to leave eastern Aleppo.
The United Nations says at least 320 civilians have been killed since the government announced an offensive on eastern Aleppo on September 22.