The shock attack comes despite a Russian air campaign targeting the group that began in September, and more than a year of strikes by a US-led coalition against the jihadists in Syria.
The Britain-based Syrian Observatory for Human Rights said Isis had killed at least 135 people in the multi-front attack that began on Saturday.
The dead included 85 civilians and 50 regime fighters, according to the monitor, which said Sunday that Isis had also kidnapped more than 400 civilians from captured territory.
"Those abducted, all of whom are Sunnis, include women, children and family members of pro-regime fighters," Observatory chief Rami Abdel Rahman said.
The monitor said at least 42 Isis fighters had been killed in the attack, adding that fighting was ongoing on Sunday, with regime forces backed by Russian air strikes trying to recapture lost ground.
It added that regime forces were bringing additional troops and military equipment from elsewhere in the city to the battlefront.
Syria's state news agency SANA said at least 300 civilians, "most of them women, children and elderly people," had been killed in the assault.
It denounced the deaths as a "massacre".
History of mass murders
The Isis assault puts the group in control of around 60 per cent of Deir Ezzor city, which is capital of the surrounding province of the same name, an oil-rich region that borders Iraq.
The jihadist group already controls most of the province, but regime forces have clung onto part of the city and a neighbouring air base despite repeated Isis attacks.
If confirmed, the death toll in the assault would be one of the highest in a single attack by Isis, though the jihadists have carried out mass murders before.
In 2014, its fighters killed hundreds of members of the Sunni Shaitat tribe in Deir Ezzor province after they opposed the jihadists.
And in August 2014, the group massacred some 200 Syrian soldiers when it overran the Tabqa military base in Raqa province.
The jihadists have also carried out mass abductions before, seizing more than 200 civilians from central Homs province in August 2014, and at least 220 Assyrian Christians from villages in the northeast of the country months earlier.
Some of those abducted in those incidents have been freed in small batches, in some cases reportedly in exchange for ransoms.
The assault came despite a Russian air campaign that began in September in support of the government, which Moscow says targets IS and other "terrorist" groups.
Isis under pressure
The Russian strikes have so far killed at least 808 Isis fighters, according to the Observatory, though they have also killed moderate and Islamist fighters and civilians, it says.
More than 3,700 Isis jihadists have also been killed in US-led coalition strikes that began in Syria in September 2014.
On Sunday, the Observatory said 40 civilians including eight children had been killed in strikes on the Isis bastion of Raqa city.
The monitor said it was unclear if the strikes were carried out by regime or Russian planes.
In recent months, Isis has come under pressure particularly from Kurdish fighters backed by US strikes, and more recently regime forces supported by Russian air raids.
On Saturday, at least 16 Isis fighters were killed in a failed attack on a government position in Aleppo province, where loyalist troops and pro-regime fighters have been advancing towards the group's stronghold of Al-Bab.
Regime forces are now within 10 kilometres (six miles) of Al-Bab, and are seeking to sever Isis-held territory in Aleppo province from that held by the group in neighbouring Raqa.
Analysts say the group regularly seeks to open new offensives when it is under pressure elsewhere.
More than 260,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests.
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