The next stage of gun changes are anticipated to be in force by the end of the year, which could see a gun register and developments in the vetting process, gun storage and licencing.
Police Minister Stuart Nash is in favour of a gun register but wants to "get it right" as other countries have struggled implementing such a scheme.
Last week, Prime Minister Jacinda Ardern announced sweeping changes to New Zealand's gun laws in the wake of the Christchurch terror attacks.
High-capacity magazines and attachments were banned along with military style semi-automatic guns.
"Within that we’ll include amnesty provisions and the buy-back, and that'll be done under urgency," Mr Nash told TVNZ1's Q+A.
"Then the next phase is actually looking at things like a gun register, the vetting process, storage, licensing itself and a number of other provisions that will not go through under urgency.
"We want to codify in legislation that in this country, it is a privilege, not a right, to own a firearm."
Q+A host Corin Dann ask about the international issues with gun registers.
Mr Nash said in principle he was in favour of a register, but was asking police for more information saying, "if we implement one... we actually get it right".
On Breakfast this morning, Ms Ardern said a gun register "on the face of it absolutely makes sense", but she was "leaning quite heavily on the police" for advice.
Other changes to vetting are being looked at, including adjusting the "fit and proper person" test, which entails police proving a person is not "fit and proper", to making the gun licence applicant prove that themselves.
Dann asked Mr Nash why there were warnings about a loophole in semi-automatic weapons during a police briefing in November 2018, challenging the Police Minister that he "did nothing".
"Not quite true," Mr Nash said. "In November last year I did ask police to have a look at the Arms Act and what we could do to actually make it more efficient, to drive changes... to give it a level of consistency that it hasn’t got at the moment."
Dann asked again what the reservations at the time were.
"The world has changed... Now, we do not believe that military assault rifles and military-style semi-automatics have a place in this country," Mr Nash said.
Dann asked if he was worried about the gun lobby at the time, "and the next part of that is what's to stop that lobby coming back?"
"I can tell you what’s to stop it coming back, and that is the fact the Prime Minister has made it very clear that these weapons will be gone," Mr Nash said.
In December 2017, Mr Nash told 1 NEWS inconsistency in the police force with how licences were given out and the storage of guns would be looked at.