A plane from the forces of renegade former Libyan general Khalifa Haftar crashed in the city of Tobruk on Tuesday, killing the pilot and a child, a security official said.
“The pilot was killed when his aircraft hit a building during a demonstration flight,” the official told AFP.
The co-pilot survived, but a child was killed and a number of civilians were injured, the official added.
Witnesses reported seeing the plane flying at a low altitude with smoke billowing from one of its engines before it struck an apartment building.
Security officials said the aircraft's hydraulic system had failed.
The impact of the crash damaged part of the building.
It comes three days after another plane belonging to Haftar's forces crashed in eastern Libya, killing a pilot.
That aircraft went down in Al-Baida, after carrying out strikes against Islamist militants at Derna, 100km away.
At the time, Haftar's forces attributed the crash to a “technical” glitch.
Ansar al-Sharia, classified as a “terrorist organisation” by the United States and Libya, said on social media networks that its fighters had shot down the plane with a missile.
General Haftar launched an assault against Islamists in the eastern city of Benghazi on May 16.
Detractors have accused his “National Army” paramilitary force of trying to mount a coup.
Libya has been awash with weapons since the uprising three years ago that toppled and killed Muammar Gaddafi, and successive interim governments have struggled to establish a strong army and police force, giving former rebel groups a free hand.
Ansar al-Sharia controls much of Benghazi, the cradle of the uprising against the Gaddafi regime. - Sapa-AFP