The Minister of Foreign Affairs and Trade in New Zealand has confirmed that no arrests were made in the shooting of Kiwi woman, Lynn Howie and British man, Mark De Salis, in Libya.

Local media agency Libya Alhurra had earlier reported that four people were arrested for the killings. However, Libyan authorities denied the reports and advised the foreign affairs ministry that no arrests were made. The investigation continues as a Kiwi ministry spokesman said efforts were being made to bring the killers to justice.

On Jan. 3, Reuters reported that a Kiwi woman and a British man were found dead with gunshot wounds near the coastal area of Mellitah, 100 kilometres west of Tripoli where a large gas and oil complex is located. The complex is owned by Italy's ENI.

Authorities discovered the bodies next to each other near their luggage. A security source told Reuters that their luggage remained intact and nothing was stolen. However, the motive for the murders remains unclear.

The victims' names were revealed on Jan 5. The New Zealand woman was named Lynn Howie, a mother with two children living in Wellington. Ms Howie was visiting Libya where she had worked as a regional health protection officer.

Ms Howie's companion was identified as British national Mark De Salis. According to officials, Mr De Salis had worked in Tripoli for 6 years as a power manager for an electric company. Both Ms Howie and Mr De Salis were found dead together.

Britain's Foreign and Commonwealth Office had also urged the Libyan government to investigate the motive behind the "execution-style" killing and bring justice to the victims' families.

On the Facebook page of the Sabratha Media Center, a photo of the alleged bodies showed a man and woman lying face down. A spread out blanket, food and drinks were seen next to them. CNN has not confirmed the authenticity of the photo but the Sabratha Medical Center said it "obtained" the photo.The police also found tire marks in the vicinity based on initial reports. The shooting incident came after a month when an American teacher was gunned down in Benghazi.