Abidi did not give a toll for the attacks but said civilians were among the casualties as the roof of a family home collapsed.
Over the past month, the self-styled LNA has been engaged in an offensive to take Derna, the only eastern town outside Haftar's control.
Derna is held by a ragtag alliance of Islamist and jihadist militias, including groups close to Al-Qaeda, hostile to both Haftar and the Islamic State group.
The coastal town is located more than 1,000 kilometres (600 miles) east of the capital Tripoli and around 300 kilometres east of second city Benghazi.
Abidi said the LNA is "advancing steadily to liberate a very small remaining pocket before liberating the whole of Derna." He said "terrorists" were "resorting to suicide attacks after they failed to tackle" the LNA conventionally.
Haftar supports an administration based in the east which opposes the internationally recognised government in Tripoli.
The strongman's critics claim he wants to establish a military dictatorship.
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