The coroner had prohibited the publication of all evidence, including the report of a Court of Inquiry, in "the interests of justice and on the basis of personal privacy".
Lt Gen Jones said the Defence Force had endeavoured to work closely with Corporal Hughes' family and to act in accordance with their wishes.
"We recognise that this has been a difficult issue for the family and our sympathies and support are with them," he said.
"The wishes of the family as expressed to the New Zealand Defence Force was not to publicly comment on this case, and to allow the family the time and space they needed to come to terms with their loss and grief."
Lt Gen Jones said the Defence Force provided personnel with psychological and physical health support before, during and after their deployment on operational missions.
He would make no further comment on the matter.
A relative of Corporal Hughes did not wish to comment, saying the family was still discussing its response.