Government forces have retaken about 80 percent of the Damascus suburb, which was controlled by armed opposition groups since mid-2013.
In footage released by Syrian state TV, Assad was seen greeting Syrian army soldiers, as they cheered the president’s arrival.
“The people of Damascus appreciate all of you for protecting the city, and we will remember this for tens of years, or even generations,” Assad told the soldiers.
“This battle has been bigger than Syria – today you are fighting this battle on behalf of the whole world,” he said.
“For each bullet you shot that killed a terrorist, you changed the balance of the world.”
Assad’s visit came as activists in Eastern Ghouta said the government arrested “hundreds” of civilians who have fled the violence in the besieged enclave over the past few days.
Activists also said that air raids continued to hit the homes of remaining civilians in the enclave on Monday, with more than 60 air strikes killing at least eight people.
The main rebel group in the area, Failaq al-Rahman, said it is in negotiations with the United Nations about a ceasefire, and said it is also asking for aid to be allowed in for the thousands of civilians that are still trapped inside.
The United Nations refugee agency says more than 20,000 people have fled the fighting in Eastern Ghouta.
The Syrian government and its allies said they are continuing to attack three rebel-held pockets of the enclave, which was, until recently, home to nearly 400,000 people.
According to activists inside the enclave, those who have made their way to government-controlled territories are often detained by government forces upon arriving at multiple points on the outskirts of the city.
“Today, there were people who were arrested in the town of Kafr Batna … men who have been leaving over the past three days are instantly being detained,” Alaa al-Ahmed, a local activist, told Al Jazeera from the town of Ein Tarma in Eastern Ghouta.
“This is because the evacuations are happening without the supervision of international bodies, they’re taking place without any guarantees,” he said.
“We’re also hearing reports of mass executions in Hamouriyah,” he said, referring to the town that has been at the centre of the fighting between rebels and military forces.
Al Jazeera has not been able to independently verify the claims.
The UNHCR office in Syria’s capital confirmed that there are three shelters in the rural Damascus area where people from Eastern Ghouta are arriving: Dwier, Hejelleh and Adra.
‘Under the rubble’
Though some aid has been distributed to people in the shelters, food and sanitary supplies are barely covering the needs of the thousands who continue to flee.
Elizabeth Hoff, spokesperson for the World Health Organization in Syria, told Al Jazeera that civilians who had stayed in underground shelters for weeks before fleeing showed symptoms of skin diseases, vitamin deficiencies, in addition to many suffering from malnutrition and chronic diseases.
Meanwhile, remaining resident inside the enclave – more than 340,000 people – are suffering from acute food shortages and a lack of medical supplies.
Ali al-Khouli, an independent journalist in Douma, one of Eastern Ghouta’s main towns, described the current situation as “uninhabitable”.
“No infrastructure, no food, no medicine, no hospitals left here in Eastern Ghouta,” he said.
“Families who left here have done so as a result of the heavy bombardment, they say it is more merciful than having to endure the government’s shelling,” al-Khouli added.
According to al-Khouli, those who chose to leave were “100 percent” certain that if they stayed, they would have lost their lives and ended up “under the rubble”.
Al Jazeera’s Zeina Khodr, reporting from Beirut in neighbouring Lebanon, said the front lines are changing and the government is regaining territory, prompting thousands to flee.
“We know that the government considers anyone in the opposition a terrorist,” she said, pointing to Civil Defence workers – also known as the White Helmets – as an example.
Both al-Khouli and al-Ahmed say that the government facilitated corridors for the evacuation of civilians, but it is unclear where the families are headed exactly.
“There are multiple locations we hear they’re being transferred to, but exact locations have not yet been confirmed,” al-Khouli said.
Activists have also noted that many would rather flee to other rebel-held territories instead.
Organisations such as Human Rights Watch, the UN, ICRC, have all called on international observers to be deployed on the ground to ensure that people are safe.
Follow Farah Najjar on Twitter: @NajjarF91