Some family members of Corporal Douglas Hughes say they want an open inquest to satisfy their questions over the soldier's death.
Coroner Gordon Matenga last week found that Corporal Hughes' death was a suicide. But he did not open an inquest and said he was satisfied with the investigation that was conducted by the Defence Force court of inquiry, details of which he suppressed.
But Corporal Hughes' uncle Mike Poa said the family held strong concerns about the Defence Force's handling of the incident.
He would not discuss the issue in detail before a whanau meeting because the family wanted to present a united front in confronting their concerns.
"We're not embarrassed by the fact he [Corporal Hughes] is gay. I just feel personally they didn't do enough to support him. My feeling is perhaps he lacked access to the assistance he deserved.
"I don't think we've been told the truth," said Mr Poa.
Corporal Hughes' mother, Venus Poa, is due back from a trip to Australia tomorrow, Mr Poa said.
The family planned to meet and discuss what steps to take now that there will be no coronial inquiry, he said.
"I just want to get to the bottom of things. The army have abdicated their responsibility."
He said the family had hoped the coronial inquiry would satisfy their questions and he was angry Mr Matenga had decided not to hold an inquest.
"It's his job to do an investigation."
Former Defence Minister Phil Goff has backed the family.
"I'm not throwing the blame on any particular individual on this," said Mr Goff, now Labour's defence spokesman.
"I'm just saying that when you have a tragedy of this nature, it's really important to learn all of the lessons of it so you can avoid it happening again.
"Only if you bring it out in the open can you seriously start to address it."
Mr Goff wants the decision overturned by the Chief Coroner or Solicitor-General, as is possible under the Coroners Act.
Corporal Hughes was serving at Romero base in Bamiyan province at the time of his death on April 3 last year in the presence of a colleague.
"This is not about a witch-hunt," said Mr Goff. "It is about finding answers which will assist the Defence Force to help prevent a death of this nature again.
"You need to get to the bottom of it, and frankly there are times when it is better dealt with outside of the Defence Force than simply through a court of inquiry.
"Fresh eyes and an outside perspective may well be of real assistance to the Defence Force in putting the right policies in place."
The family reportedly believe Corporal Hughes was bullied because he was gay and received no support from commanders.
But Defence Minister Jonathan Coleman told the Herald yesterday that he did not believe anything could have been done to prevent the tragedy.
Asked about the New Zealand Defence Force in terms of its attitude to homosexual defence personnel, Dr Coleman said he did not have concerns about the force's attitude but could not account for the attitudes of every person in the organisation.
"I don't have any concerns about the institutional framework around it."
The Defence Force has had a policy of accepting gay personnel in line with the decriminalisation of homosexuality in 1986 and the Human Rights Act 1993.
Prime Minister John Key said today he was satisfied the Defence Force had robust policy in dealing with gay and lesbian employees.
"They have a clear code of conduct and it's my expectations that they honour their legal requirements,'' Mr Key said.
About a year ago the OverWatch group was formed as a support group for gay personnel and an advisory group for Defence hierarchy. It marched in the Auckland Gay Pride Parade last month.