The fighting south-west of Derna was the most intense since Haftar’s Libyan National Army (LNA) stepped up its campaign to take control of Derna, said Milad al-Zwai, spokesman for the LNA’s special forces.
One commander was killed and two soldiers wounded, he said.
Derna is controlled by a coalition of Islamist militants and rebel veterans known as the Derna Mujahideen Shura Council (DMSC).
The LNA, which has been trying to consolidate its grip on eastern Libya after taking Benghazi last year, has encircled Derna and launched occasional air raids over the city.
Haftar announced he would “liberate” the city early this month.
According to medical sources and statements, LNA forces have lost about nine men and 14 DMSC members have been killed during recent clashes around Derna.
The car bombing took place south-west of the city of Ajdabiya, while a soldier was abducted from a checkpoint south of Benghazi, a security source said.
Islamic State later claimed responsibility for the car bomb.
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