Police Minister Judith Collins wants an investigation into gun laws to get under way quickly.
Her preference would be for a select committee or ministerial inquiry, she said.
After the shooting of four police officers in Kawerau last week and the seizure of a cache of high-powered firearms in south Auckland, both the Labour Party and the Police Association have called for an independent inquiry into the availability of guns.
Ms Collins told Morning Report there were lots of law-abiding gun owners, so an investigation should focus on how the weapons were getting into the hands of criminals and gangs.
"If we can get a cross-party support for any changes in the gun laws, that'll be really helpful, I think. It would depoliticise what's a very important issue."
Police Association president Greg O'Connor has said any inquiry would be a step in the right direction.
The association had been voicing concerns about the accessibility of firearms for some time, he said.
"The onus falls on firearms users, owners and others in the firearms industry to support such a call before there is a more serious incident involving multiple deaths," he said.
"[That would] necessitate just such an inquiry taking place, but in an emotionally and politically charged environment."
However, the Sporting Shooters Association had said calls for an inquiry were a knee-jerk reaction.