Ardern is limited in commenting much further on the case given it is before the courts.
In March 2020, Tarrant pleaded guilty to 51 counts of murder, 40 counts of attempted murder and a terrorism charge.
He was sentenced to life in prison without parole.
Victims of the attack have spoken to the Herald and said the appeal will revictimise them.
Imam Gamal Fouda who survived the terror attack at his Deans Ave mosque where 44 worshippers were shot dead during Friday prayer said he has faith in the New Zealand judicial system.
"I believe that this will cause significant trauma in our community and that the terrorist will gain nothing from it," he said.
"I am struggling to understand why he is doing this when he himself pleaded guilty.
"I cannot help but think that this is another action from this terrorist to harm his victims again by keeping alive the memory of him and his terrorist actions."
Temel Atacocugu, who was shot nine times during the Al Noor Mosque attack, hadn't heard the news of the appeal when contacted by the Herald, and said he would discuss it with his lawyer tomorrow.
"He's doing these things to keep reminding the public that 'I'm still here'.
"He's trying to not be forgotten.
"It's not going to work and he will remain in there forever."
Rahimi Ahmad who was shot at Al Noor and badly injured was today "very surprised and depressed" at the terrorist's latest move.
"I really hope that his request is not granted," he said.
"He was very lucky to have been well-treated in the prison."
When contacted by the Herald today, Tarrant’s lawyer Ron Mansfield KC said he was “not available at this time” but added he was currently only assigned as counsel for the coronial inquiry into the March 15 terror attack.