Briton, New Zealander shot dead in Libya
Libyan security force members man a checkpoint on February 3, 2013, in Tripoli
"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 said.
The bodies had been moved to Tripoli, the source added, without giving any details on the circumstances of the deaths.
Britain and New Zealand said they were seeking to confirm the report.
The British Foreign Office said it was "urgently seeking" further information following the announcement of the discovery.
New Zealand's foreign ministry said it was aware of the report and was "working with the relevant authorities to confirm this".
It added that "the bodies have not yet been formally identified and the next of kin have not yet been informed".
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.
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