Relatives of Free Syrian Army rebels, including women and children, were among those executed, CNN quoted activist Mohammad Basbous from Aleppo media centre as saying on Monday.
"Every hour, butcheries are carried out," the Syrian Observatory for Human Rights said, adding evidence to earlier UN reports of atrocities being committed against civilians.
The reports come as Syrian soldiers recaptured neighbourhoods of east Aleppo in the rebels' last stand against the government forces.
"Young people especially were executed," said Ahmad Dbais, director of hospitals for the Union of Medical Care and Relief Organisations.
Terrified residents slept on the streets after Syrian soldiers forced them out of their homes, Aleppo resident and journalist Karam al Masri told CNN.
According ot the Syria Civil Defence activist group, the White Helmets pleaded with the international community to provide safe passage out of Aleppo for their volunteers and the 100,000 civilians.
"The regime has been trying to kill us for five years," the group said on Twitter. "Please don't give them this chance."
An Aleppo resident, a "teacher, activist and reporter" inside the beleaguered city, posted a number of tweets bidding farewell to his followers.
"This is a call and might be the last call," he tweeted. "Save Aleppo people. Save my daughter and other children."
The Syrian army and its allies have aggressively pushed into the rebel sections of east Aleppo in recent days, said the Syrian government.
"It is going to be a very difficult situation because there is no place for all these fleeing civilians," said Ismail Abdallah, a member of the White Helmets.
Abdallah told CNN the al-Fardous neighbourhood has been captured by Syrian government forces, while some areas of resistance remain in parts of the city.
"There is a mass exodus of terrified civilians fleeing from al-Fardous, al-Jaloom, al-Salheine and areas that have been captured today to other areas such as al-Mashhad and Salah Eddiene," he said.
Syrian state television painted a different picture of the day's events, broadcasting video that showed residents celebrating after the government forces took control of a neighbourhood.
Earlier, SANA news agency and the Syrian Observatory for Human Rights monitoring group said the neighbourhood of al-Sheikh Saeed in southeastern Aleppo had been captured by the Syrian military.
The neighbourhood was taken from rebel forces with the assistance of government-allied groups.
According to SANA, the army units are "continuing the operations and targeting the remnants of the terrorists who fled away towards" the al-Sukkari and al-Fardous neighbourhoods.
There are also reports of civilian casualties as a result of the shelling, according to media organisations with teams in Aleppo.
The international community has failed to broker a ceasefire for the city, which appears on the brink of falling back into regime control.
Former UN Secretary General Ban Ki Moon expressed alarm over "reports of atrocities against a large number of civilians, including women and children" in a statement.
"While stressing that the UN is not able to independently verify these reports, the Secretary General is conveying his grave concern to the relevant parties."
The government controls western Aleppo and its troops have made significant territorial gains in the east since its forces entered the enclave by ground on November 27, backed by continual airstrikes.
The government has now taken more than three-quarters of the area.
Rebel groups held eastern Aleppo for more than four years after the Arab Spring uprising, and a Syrian regime siege on the area had essentially cut it off from the outside world, sparking a humanitarian crisis there.