The family of the terrorist who attacked shoppers in Auckland say they are heartbroken by the horrible act.

Ahamed Aathill Mohamed Samsudeen, a 32-year-old refugee originally from Sri Lanka, was shot dead by undercover police after stabbing six people inside Countdown in LynnMall on Friday.

A police car outside LynnMall where the attack took place on Friday. Photo: RNZ / Jean Bell

A seventh person was also injured in the attack.

In a statement released via a lawyer and credited to Samsudeen's brother, Aroos, the whānau said they wanted to send love and support to those who were hurt.

"We are so shaken by what has happened and we do not know what to do. We hope these words will help bring some peace to your beautiful country. We are ready to help you all in the healing process no matter what it is needed from us.

"We hope to find out with you all, what happened in Aathil's case and what we all could have done to prevent this. We are heartbroken by this terrible event.

"My father still doesn't know my brother is dead because he has been missing him so much and is very ill these days."

The statement said Samsudeen, who arrived in New Zealand in 2011 on a student visa, suffered from "political torture" and his mental health steadily declined over the years.

Samsudeen spent a lot of time on social media, it said.

"We saw his mental health got worse and worse during the last 10 years or so. He spent a lot of his time in prison and was always struggling with some court cases. When we heard that he was in prison in New Zealand, we thought it would do him some good but didn't realise he would spend so much time there. He also had many problems in prison."

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Members of the wider family visited New Zealand in 2013.

"We love your country and your people and we know from what we have seen since the Christchurch attack that you are good people. We want to stand with you. We have lost Aathil. We don't know what to do while our father is still very ill and doesn't know about this situation.

"Aathil was the youngest and very close to my father. He grew up with my parents in the family home while the rest of us grew up mainly in hostels. Aathil was the baby of the family. My mother is so upset."

Samsudeen's brother said there were difficulties.

"Aathil always contradicted what he was told. He would hang up the phone on us when we told him to forget about all of the issues he was obsessed with. Then he would call us back again himself when he realised he was wrong. Aathil was wrong again [on Friday]. Of course we feel very sad that he could not be saved. The prisons and the situation was hard on him and he did not have any support. He told us he was assaulted there."

The statement said the family hope they remain safe now that the identity of the attacker has been made public.

Ultimately, it said the family were thinking of the innocent people who were hurt.

"We all have to try to accept this. I pray that God will help us all to heal from this very sad day. We are thinking of you all. We are thinking of our parents. We are thinking of the boy who left us and the innocent people. Our lives have changed forever. We realise that it will take us some time to come to terms with this. We are thinking of the injured, both mentally and physically."