The Britain-based Syrian Observatory for Human Rights said the Syrian government is now in control of over 80 percent of the area near Damascus where a government offensive has killed hundreds and forced tens of thousands from their homes.
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Recapturing eastern Ghouta, which has been under rebel control since 2012, would mark one of Assad's biggest victory in the country's civil war. It would also be the worst setback for rebels since the opposition was ousted from eastern Aleppo in late 2016 after a similar siege and bombing campaign.
Assad also told soldier that the residents of the capital, who have come under repeated fire and shelling from the rebel-held areas, appreciate the military’s advances. Assad told the soldiers that they are not only fighting for the region but also to rid the world of terrorism.
"With every bullet you fire at a terrorist, you change the balance in the world," Assad said. Syria's government views all its opposition as terrorists.
It was not clear where in eastern Ghouta Assad was.
The visit comes on the week the war enters its eighth year, a war that has devastated large parts of Syria, and displaced nearly half of the population. What started as peaceful protests against his family's long rule turned into a civil war after a heavy crackdown.
The government fought the opposition for years, using its air force and artillery and solicited help from its Russian and Iranian allies, who threw their weight behind Assad.
The United Nations told Reuters on Sunday they estimate around 25,000 people have left eastern Ghouta in the past week. Civilians have been making their way out towards army positions on foot, hauling their belongings with them. They are then transferred to one of three reception centers.
The Observatory said about 50,000 had left the southern pocket in the past 72 hours and thousands left on Sunday. Russian news agencies said more than 73,000 people have left eastern Ghouta so far, 25,000 of which left on Sunday.
The Observatory also reported that Sunday saw new intense shelling on Douma, the largest town in eastern Ghouta, after days of relative calm.
Meanwhile, figures close to rebels said talks were underway with the aim of them leaving to other opposition areas or giving up arms, though rebels have publicly ruled out the kind of negotiated withdrawal that helped Assad recover Aleppo, Homs and other areas.