Kennah had flown on the weekend to the nearby El Feel oilfield and later made it to El Sharara, but failed to take control of it, oil workers have said.
Tensions there and at the nearby 70,000 bpd El Feel field have risen in past days after the LNA banned flights without its permission.
Separately, an eastern Libyan military plane intercepted on Sunday a civilian plane after it took off from the El Feel oilfield, forcing it to land in the southern region of Sebha, said a source from the eastern-based armed forces.
BENGHAZI, Libya (Reuters) - Eastern Libyan forces loyal to commander Khalifa Haftar carried out four air strikes near the El Feel oilfield as a warning to a rival commander, a field engineer said on Saturday.
CAIRO (Reuters) - East Libyan forces warplanes have struck targets near the El Feel oilfield, the al Hadath TV station reported on Saturday.