The MiG-21 fighter jet hit a block of flats near the new parliamentary building after developing a “technical fault”, a security official said.
The aircraft was controlled by forces loyal to ex-General Khalifa Haftar who have been battling Islamist militias.
The Islamist-linked Libya Dawn group seized the capital, Tripoli, last week.
Parliament had earlier relocated to Tobruk, more than 620 miles away, because of the deteriorating security situation in Tripoli.
Witnesses said the jet was flying at a low altitude and smoke was billowing out of its engine before it crashed into an apartment block and burst into flames, the AFP news agency reports.
The plane came down on September 2 around 0.6 miles from the seat of parliament, killing at least two residents and a co-pilot, Reuters news agency reports.
The dead included a child, but the co-pilot survived, an unnamed security official is quoted by AFP as saying.
Libya has been hit by instability since an array of militia groups, backed by NATO air strikes, overthrew long-serving ruler Col. Muammar Gaddafi in 2011.
The militia groups, many of whom are allied to rival politicians, have been fighting for power among themselves.
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