Mohammed Soualem, labour minister in Ali Zeidan's government from 2012 to 2014, "was directing military operations against IS" at the time, said the agency loyal to the North African country's new unity government.
He was killed in fighting in the Abu Grein area, 100 kilometres west of Sirte, the jihadist group's main stronghold in Libya and hometown of late dictator Moamer Kadhafi.
"The clashes cost the life of Commander Mohammed Soualem and wounded five fighters," LANA reported.
Last Tuesday, forces loyal to the Government of National Accord said they had retaken the key town of Abu Grein from IS.
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GNA troops and forces of the rival government based in the east of the country and loyal to General Khalifa Haftar are engaged in a race to be first to eject IS from Sirte, 400 kilometres east of Tripoli.
The rivalry between the two factions is a major cause of international concern which sees it as jeopardising anti-jihadist efforts.