The so-called Syrian Observatory for Human Rights, said Daesh had killed at least 35 members of the Syrian army forces and detained some medical staff from the hospital.
The fighting in and around the hospital also killed at least 24 Daesh militants, the Observatory said, Reuters reported on Sunday.
Daesh's Amaq news agency said its fighters staged a "major offensive" on the southwestern edge of Deir ez-Zor on Saturday, storming the Syrian Hospital and cutting the supply route between the a Syrian army base and the airport.
Daesh controls most of Deir ez-Zor province and has laid siege since March last year to the remaining government-held areas in the city of the same name, which is close to Syria's eastern border with Iraq.
Deir ez-Zor province links Daesh's de facto capital in the Syrian city of Raqqa with territory controlled by the militant group in neighboring Iraq.
Daesh also said it had taken control of a check point, a fire station, university accommodation, grain silos and some territory near the al-Tayyam oil fields, in the vicinity of the state-held military airport on the city's southern edge.
Russia's RIA state news agency on Saturday reported a source within the airbase on the southern edge of the city as saying a Daesh attack had been repelled.
The Observatory and Amaq said there were ongoing fierce clashes between army forces and Daesh State in the area of the attack.Tasnim News Agency - world