The Syrian army is pushing into the area with the support of Russian air strikes, and there are reports of civilian casualties. The Syrian government is determined to seize Kafr Batna, Saqba and the rest of the besieged eastern Ghouta region from rebels.
More than 350,000 people have been killed since Syria's conflict broke out in 2011 with protests against Assad.
The monitor said on Sunday that more than 1,500 Kurdish fighters had been killed in the two-month assault by Turkish forces and allied Syrian rebels on Afrin. "We are fighting the same way we did in Canakkale", he said, using the Turkish name for the historic battle.
The operation is being carried out under the framework of Turkey's rights based on global law, UN Security Council resolutions, its self-defence rights under the UN charter, and respect for Syria's territorial integrity, it has said.
"Will the Afrin operation actually push more local people into the arms of the YPG?"
"The medical situation is catastrophic".
"The majority of those leaving are from the Hamouriyah area, but also include some medical cases from Douma", Mysa Khalaf, UNHCR's spokesperson, said from Damascus. "It's a major challenge to reach the wounded because of the intensity of the airstrikes".
Tens of thousands have fled Afrin in recent days as Turkish forces and allied Syrian fighters have advanced.
Ali Serdar Erdurmaz, an analyst with Hasan Kalyoncu University based in Gaziantep province near the Syrian border, said the victory would embolden Erdogan, who has urged the U.S.to ensure the YPG also withdraws from the town of Manbij, further east. Others said rebels hoarded food and humiliated civilians, even shooting people trying to leave.
Rebels have repeatedly fired shells from Eastern Ghouta at government-controlled areas in and around Damascus.
More than 400 pro-Ankara rebels have been killed since January 20, the Observatory said Sunday.
Turkish authorities view the Syrian Kurdish YPG militia, which the US backs, as an extension of Turkey's Kurdish PKK militants who have sought autonomy for decades.
With such figures, the number of displaced people increased to 40,000 people who have left their homes since Friday night in Eastern Ghouta, the SOHR said.
Video posted by the Observatory showed victims lying dead in the streets in pools of blood.
The government-controlled Syrian Central Military Media said the army has declared a 24-hour cease-fire in Harasta starting Saturday afternoon in order to allow civilians to leave the area.
An exodus of similar proportions was under way hundreds of kilometres (miles) to the north in the city of Afrin, where Kurdish forces have been almost encircled by Turkish troops.
Meanwhile, the U.N. Security Council again demanded a cease-fire throughout Syria and backed a U.N. -endorsed roadmap for a peaceful transition and elections. Find us on Facebook too!
SARC did not immediately respond to CNN's request for comment.
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