Daesh militants clashed with forces guarding Libya's al-Sidra oil port on Monday, Reuters reported.
The group has also said it took control of a nearby town, and in an online statement said it also set off a car bomb during the attacks.
Libyan authorities were not immediately available to comment on the clashes or capture of Ben Jawad.
Amid fighting over the past year between rival groups in Libya, Daesh took advantage of the chaos over the fight for the country's energy reserves. Daesh has captured other cities and attacked oilfields in southern Libya, although it has not taken control of oil refineries as in Syria.
Since 2011 Libya has been divided by separate governments vying for power, one in Tripoli, and the other in eastern Libya.
The port of al-Sidra is protected by the Petrol Facilities Guard, which has backed the internationally recognized government in the east, has also clashed with other forces supporting the same government.
The UN is seeking support for a deal made in Morocco last month to establish a unity government to end the civil war in Libya.
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