There was low cloud and reduced visibility at the time of the crash and the pilots were flying on sight rather than instruments.
New Zealand's Ministry of Foreign Affairs and Trade this afternoon confirmed three bodies had been recovered and flown to Port Moresby.
But a ministry spokeswoman said formal identification of the bodies was required before they could be repatriated - a process that could take some days to complete.
"The New Zealand High Commission continues to work with Hevilift, the Australian High Commission and local authorities to provide support and assistance to the family of the New Zealander who was on board the helicopter."
Mr Annan grew up in Alexandra and had been based in Australia with his partner.
He had worked for Hevilift for more than 10 years.
Paul Booij of Hevilift said the company would co-operate with authorities and conduct its own investigation into what caused the crash.
"We can assure everyone that no one wants to know what happened more than we do. We operate in rugged terrain and challenging conditions in Papua New Guinea and we have very strict protocols within our operations.
"We take the safety of our staff very seriously, it is our highest priority. We aim to keep them all safe and to achieve that, we have rigorous maintenance schedules in place for all our aircraft; along with strict operational flight safety programs and protocols," said Mr Booij.
The search for the missing men involved seven helicopters, including those from the Australian and New Zealand Defence Forces.
The search for the missing men involved seven helicopters, including those from the Australian and New Zealand Defence Forces.