The umbrella group for Islamist militias calling itself Dawn of Libya said it has also taken hold of other locations in the capital controlled by the rival militias, drawing to a close one chapter in a prolonged confrontation between the Islamist-allied militia, largely from the city of Misrata, and the powerful militia from the western mountains of Zintan.
The fight has largely destroyed the airport and scarred the capital, prompting diplomats, foreign nationals and thousands of Libyans to flee.
It also comes as part of a backlash by Islamist factions after losing their power in parliament following June elections and in the face of a campaign by a renegade military general against extremist Islamic militias in Benghazi, Libya's second-largest city.
But this has been the worst bout of violence in the battle over turf and influence since 2011. Mysterious airstrikes have struck the positions of Islamist militias, sparking accusations by the groups that Egypt and the United Arab Emirates, who oppose Islamists in the region, were behind it.
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The commander spoke on condition of anonymity because he was not authorized to brief reporters.
The fighting on the ground has mirrored a political standoff between Islamists and the outgoing parliament they controlled, and anti-Islamist groups who control the newly elected parliament. Each considers the other illegitimate.
After claiming control over the airport, Dawn of Libya called on the outgoing parliament to convene in the capital to take "the necessary measures to protect state sovereignty.