The Douma suburb is a flashpoint town and is the largest rebel-held area on the Damascus outskirts, which the government is trying to retake.
In a report published on Monday, Assad said that his forces are on the road to victory, citing the recapture of Aleppo as a "tipping point" in his fight against Syrian rebels.
"We don't consider it [retaking Aleppo from the rebels] as a victory. The victory will be when you get rid of all the terrorists," Assad told French journalists visiting the Syrian capital on Monday.
As fighting intensifies in Douma, most field clinics have been moved to basements, and health workers worry that medical supplies are running out.
Anas Abu Malik, a volunteer medic, told Al Jazeera that he tries to avoid taking the main streets for fear of being hit by government bombardments.
Anas was a medical student when the uprising started six years ago. But he left school and joined hundreds of volunteers operating field clinics as the fighting intensified.
"The town is targeted every day with all sorts of weapons, rockets, shells, air strikes, barrel bombs. They target mostly civilian areas, markets, busy streets," he told Al Jazeera.
"Most of the times we can't rescue people because of the intense air strikes."
Fear and anxiety
Anas has recently become a father, and that has only increased his anxiety about the future of Syria.
"Every day when I leave home for the clinic, there comes this feeling that I may never come back home, or that, God forbid, my wife and my child could be killed in an air strike," he said.
Aid agencies managed to get to Douma in June for the first time since government forces besieged the town four years ago.
People in the area have refused to leave despite the siege, and they said they are still hoping the war will end.
Still, as the army closes in on the town, many are worried they might have no option but to leave their homes.
"We live in tough times. It’s very cold and we don't have money to buy wood to heat the house. Our kids suffer a lot," a patient in one of the underground hospitals told Al Jazeera.
The capture of Aleppo by government forces has sent shockwaves in rebel-held areas, said Al Jazeera's Hashem Ahelbarra, who is reporting in Gaziantep near the border with Syria.
"Many now believe that as the international community seems to be showing less desire to get involved in the Syrian conflict, President Assad may continue his push to reclaim more territory."
The nearly six-year civil conflict has killed more than 310,000 people, and forced millions of Syrians to flee the country and become refugees.
Author: Al Jazeera News