The strikes followed a ground assault with infantry and clashes earlier in the day that left five dead. Both actions seemed to be part of a plan by Gen Khalifa Hifter and his forces to seize control of the eastern city.
The official said Hifter's forces lost four fighters while a member of an Islamist militia also died in the fighting. He spoke anonymously because he was not authorized to speak to the media.
The official said Hifter's forces were met by fire from Islamist militias in the neighbourhoods of Siddi Faraj and Qawarsha. It appeared to be the first time Hifter's forces have made a concerted ground assault on parts of the city.
They previously have launched attacks from Benghazi's outskirts and carried out limited airstrikes.
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Today's airstrikes were carried out using helicopters, the official said. It was not immediately clear what the specific targets were.
The fighting has escalated the crisis in Libya, which has been embroiled in turmoil since the 2011 civil war and the downfall of longtime dictator Moammar Gadhafi. Heavily armed militias, born out of the rebel groups that toppled Gadhafi, are now the main power in the country.