A man in his 60s died and two adults and two children were injured after being thrown from their boat near Pauanui in the Coromandel on January 5 during a horrific boating incident.
The two children were flown to Starship hospital in a critical condition with their mother, while the male survivor was treated on the ground in a moderate condition.
The family said they have been "inundated" with support.
"Our family will now await the outcomes of the current investigations so we have a full and accurate understanding of why this happened."
Almost two weeks after the tragedy the boy and girl have now woken from their induced comas but still face a long road to recovery, according to a Givealittle page set up by a friend of the family.
One of the children is still in ICU fighting infections, while the other is making good progress in a ward.
But with both children still in hospital, they still face a long road to recovery, with many unknowns.
"Our young family members continue to receive wonderful care in Starship Children's Hospital and we want to extend our appreciation to the hospital staff.
Our family will now await the outcomes of the current investigations so we have a full and accurate understanding of why this happened."
Aucklander Campbell Wright was on a boat going out fishing when he saw 20 to 30 people in the water trying to right the stricken vessel, which he estimated was about 5m long.
Speaking with the Herald at the time, he said it took a lot of people and a long time to get the boat upright.
"There was a big cheer when they got it over."
Along with the rescue helicopters, two ambulances, two managers and a rapid response unit were sent to the Vista Paku area to help.