The Prime Minister says the alleged Christchurch gunman should not have been able to send a letter expressing his "hateful views" from behind bars.

Her comments come after it was revealed the man accused of the Christchurch mosque shootings was wrongly able to send a letter from prison.

A handwritten letter signed by the 28-year-old accused Christchurch gunman is circulating the internet.

He writes about his political and social views but says he cannot go into great detail about his regrets or feelings "as the guards will confiscate my letter if I do (to use as evidence)".

It's understood to be a response to a letter sent to the alleged Christchurch mosque killer by a person named Alan who is said to live in Russia.

Speaking to media in Tuvalu, Jacinda Ardern said she felt the same way as everyone else in New Zealand about the issue - it should not have happened.

"I know that the Minister has expressed to corrections his disappointment and his expectations."

Corrections Minister Kelvin Davis would be taking a look at whether or not New Zealand's laws were fit for purpose.

Those laws were around how to deal with someone of this nature - "a terrorist who is seeking to share hateful views and finding platforms to share those views".

The Government needed to make sure New Zealand's laws were fit for purpose in that regard, Ardern said.

But she would not go as far as saying New Zealand's prison facilities were not equipped to handle the alleged gunman.

It was clear something had gone wrong - but Corrections itself had acknowledged there was a failing, she said.

"Obviously, this is an offender who has a very specific goal in mind in terms of sharing his propaganda so we should have been prepared for that."

She "absolutely" expected systems would be tightened to avoid a repeat of the incident, saying Davis was following up on that.

"I think every New Zealander would have an expectation that this individual should not be able to share his hateful message from behind bars."

In the letter, the alleged gunman talks about his travels in Russia and refers to it as his "favourite place in the world". He says he wishes he could visit Russia again someday but "life isn't about travelling".

The accused gunman's letter thanked his correspondent for the postage stamps, saying they were "the only two pieces of colour in my otherwise grey cell. I will have to hide them from the guards."

Corrections, in a statement, said it acknowledged that "this letter should have been withheld".

"Corrections is legislatively required to manage prisoners in accordance with the provisions set out in the Corrections Act 2004 and our international obligations for the treatment of all prisoners," a Corrections spokeswoman said.

Every prisoner had legislatively required minimum entitlements under the Corrections Act.

"One of these minimum entitlements is to send and receive mail. In accordance with section 108 of the Act, a Prison Director can only withhold a prisoner's mail in a very limited range of circumstances. Some letters have been withheld.

"We have made changes to the management of this prisoner's mail to ensure that our robust processes are as effective as we need them to be."

In a statement, Davis said his department should not have allowed the letter to be sent. He had asked questions about whether current laws were fit for purpose.

"We have never had to manage a prisoner like this before," he said.

He said New Zealanders would be surprised to hear this alleged offender was allowed to send and receive mail – "but there are rights every prisoner has under the law as it stands".

Corrections had the power to withhold some correspondence, Davis said.

"They have used this power to withhold some correspondence the prisoner has attempted to send, and some he was to receive."

Davis did not believe Corrections should have allowed the letter to be sent.

"I have made myself clear that this cannot happen again."

National's Corrections spokesman David Bennett said Davis should demand answers from officials about how the letter was sent from inside the country's maximum security prison.

"This man is accused of carrying out one of the most heinous crimes in New Zealand history. New Zealanders will be horrified that Corrections allowed him to send a letter which ... has subsequently been posted online."

Davis owed New Zealanders an immediate apology, Bennett said.

"Corrections has acknowledged this letter should have been withheld. The rights of the victims in this case and respect for them should be put above everything else."

The accused gunman's letter details his travels overseas, which included a visit to Russia in September 2015.

"It's been four years since I visited Russia and my memory is failing.

"I think you can still find some of the photographs I uploaded to facebook, though you will have to google search for an archived or saved version of my facebook page as facebook deleted my profile."

Revelations about the letter have emerged on the eve of the alleged shooter's next court appearance at the High Court at Christchurch.

The alleged killer faces 51 charges of murder and 40 charges of attempted murder and one charge laid under the Terrorism Suppression Act.

He has pleaded not guilty to all charges.

The charges relate to the killing of 51 Muslims at Masjid Al Noor and the Linwood Islamic Centre during Friday prayer on March 15.

Tomorrow marks five-months since the tragedy.