The remains of 36 people are eligible for repatriation: 29 in Malaysia and Singapore, two in Fiji, one in American Samoa, two in the UK and two in Korea.
The repatriation was triggered by a petition on behalf of the group Families of the Forgotten Fallen, from former soldiers Paul Thomas and Andrew Peters, calling for the Government to bring home the bodies of New Zealand soldiers and their children who are buried in non-Commonwealth war cemeteries.
Thomas served the Defence Force in the 1960s and 1970s, including in Vietnam. The petition came after a request from his mother to bring home his brother Adrian, a member of the original SAS squad, who was killed in action and buried in Kuala Lumpur, Malaysia, in 1956.
Peters also served in Vietnam, and is related to soldier Ike King, buried in Terendak, Malaysia.
Previously, repatriation was publicly funded for burials after 1971. Between 1955 and 1971, families had to cover those costs, and before that, personnel were buried close to where they died and not repatriated.
The previous National-led Government changed the policy, and decided to put $10 million towards the repatriation.
Mark said $10m had been set aside, but he expected the process to cost no more than $7m.
"The repatriations are planned to begin in May and all going well will be completed by October. We want to make this process as dignified and as peaceful as possible for the families," Mark said.
Last year, Vice-Chief of Defence Force Air Vice-Marshal Kevin Short told the Foreign Affairs, Defence and Trade select committee in November that 25 Army and two Air Force personnel and one child buried in Singapore and Malaysia would be coming home this year.
Five families had decided not to repatriate, Short said.
He said at the time that service medals for the fallen were also being considered.
New Zealand disinterment teams - including archaeologists, forensic anthropologists and dentists - are working with the Malaysian armed forces to reconcile the remains of the 28 bodies.
"It is a big issue for Malaysia, because they recognise that these people have died in support of their independence," Short told the committee.
He said a large ceremony involving senior ministers and Defence Force staff was expected before the remains leave Malaysia. There would be a ceremony once the remains touch down in New Zealand before they are handed back to the families.