The terrorists were now some 40 kilometers from the port, which they fired at on Monday killing several guards and wounding dozens more, the agency wrote, quoting a representative of Ibrahim al-Jathran's Petrol Facilities Guard, a federalist armed faction, which protects Es Sider.
The port, which remains under the control of Libya's internationally recognized government, has been closed for over a year as a result of the latest Libyan civil war between secular and Islamist factions.
Daesh has seized some territory around the central coastal town of Sirte, but has not been able to gain control of oil facilities.
Daesh terrorists have gained ground in Libya as a result of the civil war, which began after the NATO-assisted ousting of long-time leader Muammar Gaddafi.
The group previously attacked the same installation in October, clashing with forces protecting the terminal at one of its gates.