Fierce clashes have relentlessly rocked the city's northern edges after a multi-front offensive on Saturday that cost the lives of dozens of people.
IS jihadists overran Al-Baghaliyeh, one of the last areas on the city's outskirts known for the production of food.
The extremists now control 60 per cent of Deir Ezzor city, intensifying a siege that had already caused fear and hardship for the roughly 200,000 people still living inside.
"People are afraid, the situation is very difficult," said Attiyeh, a resident of Deir Ezzor who spoke by phone from the city.
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"Food and vegetables are rare, and we're starting to have problems with bread," he added.
He referred to reports circulated by state media that IS fighters had killed 300 civilians.
"If the city falls there will be a massacre," he said.
On Saturday, IS launched a bloody offensive on Deir Ezzor, with dozens of its fighters carrying out suicide bomb attacks as they stormed government positions.
The group also said at least 70 IS fighters had been killed in the assault and clashes, with the jihadists seizing territory inside and outside of the city's northwestern tip.
In addition, the Britain-based monitor said the jihadists had killed at least 85 civilians and kidnapped 400 more.
Ghaleb al-Haj Hamdo, 23, told AFP he can still hear the boom of clashes nearby, reminding him of the violence wreaked upon his city at the weekend.
Fearing fresh violence, residents are limiting their activities around the city at night, said the university student, who lives in the central Al-Joura district.