Corrections boss Christine Stevenson says the law should be strengthened to give the department more legal grounds to withhold prisoners' mail.
And she has set up an 0800 number and email for people to use if they receive letters from prisoners that they don't want.
The number is the latest response to the damaging revelations last week that a letter from the accused Christchurch terrorist had been sent and posted online that should have been blocked.
Another one of his letters, which was withheld, has also been passed on to police for further investigation.
Corrections had also failed to withhold two letters from Christchurch white supremacist Philip Arps, who is in prison for sharing the mosque shooting video.
Cabinet today will consider the failures by Corrections last week, but Corrections Minister Kelvin Davis would not discuss any details this morning, including whether he thought any law changes were needed.
But he said Corrections had had problems with prisoners' mail going back to 2010, and that had to be fixed.
The law includes a number of reasons to withhold a prisoner's mail, including grounds that it could endanger someone, encourage an offence, threaten or intimidate a person, or pose a threat to the security of the prison.
But Stevenson said it could be strengthened.
"The law as it stands gave us sufficient grounds to withhold the letter [from the accused Christchurch gunman] that went out, but it is possible that the law can be made a little bit clearer.
"It's about being a little bit more permissive about what we can withhold."
She has put in place a new multi-layered process for dealing with the accused's mail, which she will have to sign off.
She has also centralised all mail to and from prisoners with extremist views so that the mail can be vetted more closely.
This morning she announced a further measure to stop inappropriate mail being sent.
People who receive correspondence from prisoners they don't want can call 0800 345 006 or email email@example.com.
"If any people in the community are receiving letters from prisoner they do not wish to receive, or regard as harmful, can they please ring that number or email us and we will put a stop to it as best we can."
She said there were 15,000 items of prisoner mail every week.
"There will be things that may slip out that we are not aware of. People can reach out to us and we can put a stop to it.
"We will have to be more vigilant, but could I please again apologise most sincerely for the distress this has caused. Public safety is at the heart of what Corrections does and we failed our own high standards last week."
She said she will have to consider how to punish a prisoner who has sent inappropriate mail when that scenario arises.
National Party leader Simon Bridges said that the law was already sufficient and nothing needed to be changed.
"Both Kelvin Davis and Corrections bosses have said the letters shouldn't have been sent. That is an acknowledgement that they could have been stopped under the current laws.
"What's happened in the case of the alleged Christchurch gunman and another prisoner with extremist views came down to incompetence from Kelvin Davis and Corrections."