"The bodies of a British man and a New Zealand woman who had been killed by bullets were found on the beach in Mellitah on Thursday afternoon," the source told AFP.
The bodies had been moved to Tripoli, the source added, without giving any details on the circumstances of the deaths.
"We are aware of the tragic death of a British national in Libya and we stand ready to provide consular assistance," a spokesman for Britain's Foreign Office told AFP today.
It added that "the bodies have not yet been formally identified and the next of kin have not yet been informed".
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The Mellitah area houses a major gas complex run by Mellitah Oil and Gas, a joint enterprise of Italy's ENI and Libya's state-owned National Oil Company, which exports natural gas to Italy through the Greenstream pipeline.
Libya has seen growing unrest following the overthrow of long-time dictator Moamer Kadhafi in 2011.
The country is awash in weapons looted from the slain dictator's arsenals, and many former rebel brigades have refused to disarm or join the new security forces.