Four people in have been arrested in relation to the execution-style shooting of Wellington woman Lynn Howie in Libya, according to an unconfirmed local media report, relayed through the BBC.
The Ministry of Foreign Affairs and Trade has yet to corroborate the story.
Ms Howie (47) - a divorced mother of two early teenage boys who worked as a health protection officer and volunteer paramedic for Wellington Free Ambulance - was visiting Mark de Salis (48), a Briitish ex-pat who worked as a manager for First Engineering in Libya
Mr de Salis' family said in a statement that Ms Howie was a "close friend" of the oil company executive.
On Thursday, the pair were found dead lying face-down beside a picnic blanket, shot in the back of the head, on a beach near the town of Sabratha, around 100km west of the Libyan capital of Tripoli and famous for its ruined Roman city.
They had reportedly hired a car to take advantage of the good weather over Christmas to visit the beach, which is popular with locals and ex-pats.
No immediate motive has emerged for their murder, but the area has reportedly been tense since the arrest last week of four armed US servicemen, who were stopped after an argument at a nearby checkpoint. The four, who were attached to the US embassy, were later released amid speculation in Tripoli that they were checking on a radical militia based in the area, according to a Guardian report.
Two years after the ouster of Muammar Gaddafi, Libya continues to suffer from a chronic absence of security and law and order, with almost daily assassinations, bombings and kidnappings, according to a recent BBC analysis of faction fighting - which involves a mix of tribal leaders, armed militias who did not give up their weapons after the civil war, and Islamic extremists.
Violence has recently been escalating. Last month American chemistry teacher Ronnie Smith, 33, was shot dead in the eastern city of Benghazi by gunmen in a car as he went jogging near his home. Mr Smith had posted tweets relating his concern about Islamist radicals after a spate of killings in the city.
And two weeks ago their was the first reported suicide attack as a a truck bomb was exploded at an army checkpoint in the eastern city of Benghazi in December, killing 13 soldiers.