Fierce clashes have 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 agricultural areas on the city's outskirts known for producing food.
The extremists now control 60 percent of Deir Ezzor city, intensifying a siege that had already caused fear and hardship for the roughly 200,000 people still living inside.
Around 70 percent of the city's remaining residents are women and children, according to the United Nations.
"People are afraid, the situation is very difficult," Attiyeh, a resident of Deir Ezzor, said by phone from the city.
"Food and vegetables are rare, and we're starting to have problems with bread," he added.
He said reports circulated by state media that IS fighters had killed 300 civilians in the city had sparked even more fear.
"If the city falls there will be a massacre," Attiyeh said.
IS launched a bloody offensive on Deir Ezzor on Saturday, with dozens of its fighters carrying out suicide bomb attacks as they stormed government positions.
The attack and subsequent fighting has killed at least 120 members of government forces, many of whom were executed by IS, according to the Syrian Observatory for Human Rights monitor.
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.
The Britain-based monitor said the jihadists had also killed at least 85 civilians and kidnapped 400 more.
Signup to our newsletter and follow us on Facebook and Twitter!
IS on Tuesday freed 270 of the civilians -- including women, children under 14 years of age, and elderly -- after questioning them and concluding they had no ties to Syria's regime, the Observatory said.
- 'Severe' shortages -
Resident Ghaleb al-Haj Hamdo, 23, told AFP the boom of nearby clashes could still be heard in the city.
"I am afraid of a massacre that will repeat itself over and over if Daesh invades our neighbourhood," Hamdo said by phone, using an Arabic acronym for IS.
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.
The IS advance is just the latest encroachment on the city, where the government has clung to several neighbourhoods and the nearby military airport despite IS control of the rest of the province.
On Monday, IS consolidated its gains on the city's edges, taking advantage of a dust storm that all but grounded Russian warplanes that had been carrying out strikes in support of regime troops, according to Observatory chief Rami Abdel Rahman.
Since early 2015, IS has blocked off access to most of the city, leading to "a severe shortage of food, medicine, and basic commodities," according to the United Nations.
Its most recent offensive "is putting thousands of people in the line of fire," said Linda Tom, spokeswoman for the UN's Office for the Coordination of Humanitarian Affairs, or OCHA.
"The UN has received credible reports of the execution and abduction/detention of civilians, including people believed to have been smuggling food into the besieged city," she told AFP by email.
In an update published just before the attacks, OCHA said landmines lined the roads leading out of Deir Ezzor and that a majority of inhabitants were surviving on bread and water.
Syria's government airlifted basic supplies into the city on January 11, and the Russian government said a few days later it had also dropped aid into besieged neighbourhoods.
Deir Ezzor city lies about 450 kilometres (280 miles) northeast of Damascus and is the capital of the oil-rich province of the same name which borders Iraq.
More than 260,000 people have been killed in Syria's conflict, which erupted nearly five years ago with anti-government protests.