Col Mohammed Hegazi told The Associated Press that the bombers targeted checkpoints 1 kilometre away from the Benina airport in Benghazi.
The airport is the only site still under the control of renegade Gen Khalifa Hifter after he was defeated by a coalition of Islamist militias, including the extremist group Ansar al-Shariah. That group is blamed for the deadly September 12, 2012, assault on the US Consulate in Benghazi that killed US Ambassador Chris Stevens and three other Americans.
A spokesman of the February 17 brigade, part of the Islamist coalition, told Libyan television station al-Nabaa that nearly 10 of its fighters were wounded in clashes near the airport.
Mohammed Eissa also said the airstrikes had no effect on their advance as clashes continued.
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Benghazi fell under the control of the Islamist militias months ago after they repelled attacks by Hifter.
Libya is witnessing its worst spasm of violence since its 2011 civil war.
A second, parallel campaign by Islamist-allied militias swept through the capital, Tripoli, forcing rival militias, who declared their alliance with Hifter, to withdraw.