Corrections are making changes to the management of prisoner mail after letters from the Christchurch terror attack accused were published on a website.

An independent review into the prisoner mail system was released today, and Corrections chief executive Christine Stevenson said all 13 recommendations had been accepted.

It came after prison staff allowed two high-profile inmates to send three letters which should have been withheld.

Two of the letters were sent by the alleged Christchurch shooter Brenton Tarrant, and another by Christchurch businessman Philip Arps, who was jailed for sharing the mosque shooting video.

One of the letters sent by Tarrant was published on a Russian website. The letter sent by Arps to a media organisation included threats against Prime Minister Jacinda Ardern and praised Norway's mass killer Anders Breivik, Newshub reported at the time.

"We estimate around 15,000 items of mail are sent to and from prisoners each week, Stevenson said.

"It is a fine balance to uphold our lawful obligation to meet prisoners' statutory entitlements while mitigating the potential risks posed by prisoners who may wish to cause harm to others.

"In August, following the publication of a number of letters by prisoners, including the Christchurch accused, I made it clear that I did not have confidence in our existing processes for reviewing and assessing prisoners' mail. I called for an immediate review into this practice.

"I want to again reiterate my unreserved apology for the distress these letters have caused."

She said she was confident the changes they were making as a result of the review would reduce the ability for mail sent and received to cause harm or distress, either directly or indirectly.

The review found that too many individuals were involved in outgoing mail processes and some prisons were not well-resourced to manage the huge volume of mail. It also found some improvements in the legislation and regulations governing this area that could be made.

Some changes had already been made, including regular audits of mail processes and the decision-making around which letters get withheld or released.

Guidelines had also been introduced for scanning and withholding mail, gang mail, and content of a sexual nature. Prisoner mail was now clearly be labelled as such so the recipients could contact Corrections if they did not want to receive it.

Further changes included possible law changes which would cover the reading, copying and storing of mail in prison.

Prisoners who had been identified as having potentially extremist ideologies or registered victims had been centralised until Corrections had confidence the new process was working as intended.

All of Tarrant's mail was blocked while the review was taking place.