At least four people were killed and 10 wounded in clashes between the Islamist Fajr Libya (Libya Dawn) and fighters loyal to the government around the Mitiga air base, the sources said.
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An airport official said that Mitiga was closed to air traffic due to the violence.
Libyan carriers moved civilian flights to Mitiga after Tripoli's main international airport was damaged by fierce fighting between state-backed fighters and Islamist militias in July.
More than three years after dictator Moamer Kadhafi was toppled and killed in a NATO-backed revolt, Libya is awash with weapons and powerful militias, and run by rival governments and parliaments.