The government will turn "quite quickly" to reforming the vetting process and looking at gun registration but this work would not be rushed, Prime Minister Jacinda Ardern says.
The committee tasked with hearing the bill banning most semi-automatic rifles has recommended only minor changes as it fast tracks its way into law after the terrorist attack on two Christchurch mosques last month that left 50 people dead.
The legislation, which has the support of all the major parties, is on course to be passed a month after the attacks, causing some gun owners to complain there has not been enough time to make submissions, and worries from the Law Society about possible unintended consequences of rushed legislation.
Ms Ardern told Morning Report the work to ban military style semi-automatic weapons and assault rifles was just the first tranche of the work, and gun laws needed wider reform.
"I do believe there's a wider piece of work to be done around the way in which people are able to obtain licences.
"I do think it needs to be tightened up, but that's something we will go through a full process on, I know people will want time to have their say."
Once the gun-ban laws were passed the government would turn "quite quickly" to the second tranche, likely to be this year and before the Royal Commission reports back.
This second part would have a full select committee process and public consultation, Ms Ardern said.
It would look at things like the process someone goes through to be allowed to own a firearm, and gun registration.
"These are policy debates where actually it may, from some people's perspectives, not be quite as black and white.
"For me the issue of military style semi-automatic weapons is black and white and therefore should be something we could move quickly on - and have."
Ms Ardern said the majority of the feedback during the select committee looking at the gun ban had been supportive, and she was yet to hear people refuting the substance of what was being progressed.
Instead it was focussed on the process - that it was being done to quickly.
The main groups representing gun-owners have refused to comment on the report until they have considered it.
The chairperson of the committee that heard the submissions, Michael Wood, said most were in favour of the bill.
He told Morning Report about 60 percent of submissions to the Finance and Expenditure Select Committee agreed with the legislation, 27 percent expressed opposition and the remainder were unclear.
There was strong cross-party engagement, and broad support among MPs on the committee for the legislation.
"I feel that we've done a thorough job and done justice to the process even though it's been a short process."
Police association happy competition shooting exemption rejected
Police Association president Chris Cahill told Morning Report submitters' support for the bill was pleasing.
Mr Cahill said the association's biggest concern had been that the committee would recommend too many exemptions to the ban on military-style semi-automatics and the association was relieved it rejected calls to exempt competitive shooters.
"We believe [it] would have been too big a gap and would have allowed these rifles to remain in New Zealand".
Vetting overhaul needed, but will be costly - researcher
Gun policy researcher Hera Cook from Otago University said the vetting system needed an overhaul and it would be an expensive system if it was done properly.
Dr Cook said there had been little funding for training the part-time vetters administering the system.
"They tend to be looking for older people with previous experience of firearms, and the police have just relied on that rather than trying to train them to look for unconscious bias or racism - the tendency to go easy on people like yourself."
Local firearms officers need proper computer systems and should have enough time to do administrative tasks.
"It's all basic stuff, it's about putting the money in, really."