The Observatory said that almost 200,000 people have fled the region of Afrin in recent days and entered government-controlled areas nearby, adding that 11 people were killed Saturday when a shell hit a truck carrying fleeing people.
The Britain-based Syrian Observatory for Human Rights said government and Russian forces had been bombing rebel-held areas outside Damascus throughout Friday, killing 64 people in Kafr Batna and another 12 in Saqba.
Syrian State TV broadcast footage of men, women and children walking along a dirt road near the town of Hammouriyeh, many of them carrying bags, to escape rebel-held areas.
The Observatory said 30 people were killed Saturday morning in an airstrike on Zamalka that hit a group of people trying to flee into government-controlled areas.
The U.N. secretary-general said Friday he is "deeply concerned" about Syrians fleeing in a mass exodus from Afrin and another rebel-held enclave, eastern Ghouta, outside Damascus.
Thousands of people left eastern Ghouta on Saturday alone as government forces stepped up an offensive on the rebel enclave, according to Syrian and Russian officials.
Syrian government forces stepped up their offensive in the rebel-held eastern suburbs of the capital, Damascus, capturing a major town and closing in on another under the cover of Russia's air power.
Moscow's strikes also killed a dozen rebels from the Faylaq al-Rahman faction controlling the area, including two top commanders, the monitor said.
According to the Turkish General Staff, the operation aims to establish security and stability along Turkey's borders and the region as well as to protect Syrians from the oppression and cruelty of terrorists.
On Saturday, a Turkish air strike killed 11 civilians in the city as they tried to leave, it said.
Turkey launched the cross-border offensive in January against the Syrian Kurdish YPG fighters who control Afrin.
Hospital director Jiwan Mohammed told state news agency SANA the strikes had put the hospital - until then, the city's only functioning medical facility - out of service.
An estimated 12,000-16,000 people had left eastern Ghouta in recent days, while fighting in the Afrin region had reportedly displaced more than 48,000, said Linda Tom, a spokeswoman for the United Nations humanitarian affairs office (OCHA) in Syria.
The Turkish military denies the allegations, saying it has not carried out attacks that would harm civilians.
"We could see flames throughout the market and people who caught fire running and screaming", the activist said via a WhatsApp call.
"Queues of anxious families stretching for several hundred metres streamed towards the last remaining exit in the city's south on Friday, as the Turkish military and members of an Arab proxy force, which it mobilised seven weeks ago, consolidated positions they had gradually taken since Monday", the newspaper said. Since half the month of February the military units, headed by elite Tiger forces, intensified their antiterrorist operations in the region of Eastern Ghouta, east of Damascus, against extremist bands as the Al-Nusra and the Army of Islam. Mobile clinics were open and some people were taken to hospital in the capital, it said.
"Afrin is being exterminated and destroyed".
President Tayyip Erdogan said Turkey had "largely solved the Afrin issue".