In the six-page letter, reportedly uploaded to the website 4chan, the 28-year-old responded to one sent to him from a person named Alan, who was believed to live in Russian Federation.
"On review, we acknowledge that this letter should have been withheld", the department said in a statement.
Corrections is aware of the recipients of the seven letters he had sent.
Corrections' chief executive Christine Stevenson apologized for the distress that the incident has caused to people impacted by the shootings, which happened on 15 March.
"We should have been prepared for that", she said.
Part of the letter included what has been described as a "call to arms".
"We've been working with a range of people with expertise since March".
"I'm taking responsibility, I'm fixing the problem, I will turn my mind to the employment matters next week".
"He sought many things from his act of terror, but one was notoriety", she said. "This will include external membership from parties with highly specialised knowledge and experience", Ms Stevenson said.
However, he warned that this was a special case and should be a short term fix.
Corrections Minister Kelvin Davis said Corrections had made a mistake and should not have allowed the letter to be sent.
"We have never had to manage a prisoner like this before and I have asked questions around whether our laws are now fit for objective and asked for advice on what changes we may now need to make", the minister said, according to TVNZ.
He said it was a serious matter and was very re-traumatising for the Muslim community.
"We have never had to manage a prisoner like this before - and I have asked questions around whether our laws are now fit for goal".
"Almost in every circumstance you could imagine in open society, law is not black and white".
"I will have to hide them from the guards", he added.
"I think the process should have been adequate, it has proven to be inadequate".
Corrections has received advice from two officials from Norway's Correctional Services who have dealt with convicted white supremacist terrorist Anders Breivik.
One of the experts the Royal Commission into the attacks has consulted, University of Oslo's centre for research on extremism director Tore Bjørgo, was involved with the Anders Breivik case and told Morning Report Breivik's ability to communicate is strictly controlled. He remains in jail ahead of his trial, which has been scheduled for next May. "He has been able to send some letters to public figures and the police and so on but not to outsiders".
Christchurch Crown solicitor Mark Zarifeh said they are in discussions with court officials about potentially delaying the trial by three to four weeks "at the most".
Tarrant did not appear via video-link as he had at previous court hearings.
Tarrant's lawyers could not immediately be reached for comment Thursday on why they wanted to change the trial venue. I am really anxious about the repercussions of this.
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