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Four people have reportedly been arrested in connection with the execution-style killings of New Zealander Lynn Howie and Briton Mark De Salis in Libya on Thursday.
The two were apparently killed by gunshots to the back of the head near the city of Sabratha.
Local news source Libya Alhurra reported that four people have been arrested in connection with the killings.
The report could not be corroborated and New Zealand's Ministry of Foreign Affairs and Trade (MFAT) said it was not aware of any arrests but would be looking into it.
MFAT has been scrambling to remove a photograph circulating online purporting to show the bodies lying on the beach next to what appears to be a picnic blanket.
A spokesman said this would be highly distressing to the victims' families.
"An investigation by the Libyan Authorities into the deaths is underway and we will be following this closely on behalf of the family,'' MFAT said in a statement.
"We are grateful for the support from British Embassy staff in Libya who have provided assistance and we will continue to work closely with them.''
Britain's Foreign and Commonwealth Office said in a statement it was deeply saddened by the "murder'' of the two.
"Our Charg d'Affaires has raised the shooting with the Libyan authorities and we are liaising closely with them on follow-up. We call upon the Libyan Government to carry out a thorough investigation in to this tragic incident and to continue to do all it can to bring to justice the perpetrators of this appalling crime, as it strives to build strong rule of law in Libya.''
According to her LinkedIn profile, Ms Howie, 46, was a regional public health protection officer working in Wellington and Wairarapa.
The same website said she had previously worked with St John Ambulance, the Ministry of Health and Wellington Free Ambulance.
She had previously studied at Britain's Birmingham University, doing a Master of Science in Environmental Health between 2003-06.
Early today Mr De Salis' family released a statement in the UK saying they were "shocked and devastated''. They said the New Zealand woman was his "close friend'' and "our thoughts are with her family at this sad time. He will be sadly missed by his family and friends.''
Dianne Alpers, a New Zealander living in Libya, said local word was that it was a case of a "wrong place, wrong time scenario''.
"Rules are, you don't go out after dark or travel alone to isolated places east or west of Tripoli.''
For the 20 or more New Zealanders who lived or had visited Libya over the last five years or so, the benefits there were immense.
"Drenched in sunshine ... 360 days a year, Roman Ruins (Leptis magna, Sabratha), Exotic experiences - local hospitality - weddings, cuisine (Libyan soup, baby camel and cous cous aljarra-style); Mediterranean diet, The Medina (old city), date palms, citrus and olive groves...and a minimal cost of living.
"Libya's one of the few places I can work full time at 65, and despite having to forfeit my NZ pension, it's worth it. I've told my family if I'm killed in the desert, at least I'll die warm... and there's no need to cart me back to NZ.''
It is understood Ms Howie was a visitor and not working there. Mr De Salis' family said he had been working in Tripoli for six years for First Engineering as a power manager, bringing generators to the city to provide electricity.
"Mark enjoyed his work in Tripoli and liked the Libyan people. Mark had travelled extensively. He was a decent and incredibly loyal man and he was loved by many,'' the statement said.
MFAT has issued an official warning against travel to Libya due to the extreme risk of terrorism and kidnapping. Five New Zealanders are registered as being in Libya.