National response and operations manager Superintendent Chris Scahill said the last thing anyone wanted was another tragedy.
Mr Scahill said it was time for hunters to have another look at the safety rules.
"These incidents are a tragic reminder of the risks and the potential for things to go very wrong, very quickly, whenever handling firearms, and our thoughts are with the families of those who have lost loved ones," he said.
"And with the improving weather and longer daylight hours, many others including trampers, walkers and track workers, are also out and about...the last thing we want is to be dealing with another tragedy."
He said police hoped everyone could continue to enjoy the outdoors this year without any further accidents.
Safety council chief executive Mike Daisley said the organisation was thinking of the families and friends who knew Connor or Mr Ngamoki.
The pair were the latest of six non-intentional firearm deaths so far this year, he said.
"Six too many," Mr Daisley said.
"When there has been an incident, chances are that one or more of the seven [basic firearm safety] rules have not been followed. A moment's distraction can be enough to turn many lives upside down."
Mr Daisley said the council was starting to use data and evidence to develop safety initiatives which would hopefully reduce the number of hunting injuries and fatalities.
Increased education had a greater role to play than legislative change, he said.
"With firearms, as with many outdoor activities, there is always the potential for things to go wrong. Tragic incidents often come down to human error and can be the result of one action or decision," Mr Daisley said.
Firearm users were responsible for their own safety and that of others in their hunting party or vicinity, he said.
The New Zealand Mountain Safety Council delivers the firearm safety programme nationally in partnership with New Zealand Police.
Firearm licence applicants are required to pass firearm safety courses and testing before gaining a licence.
The Firearms Safety Code: Seven Basic Rules of Firearms Safety
1) TREAT EVERY FIREARM AS LOADED
2) ALWAYS POINT FIREARMS IN A SAFE DIRECTION
3) LOAD A FIREARM ONLY WHEN READY TO FIRE
4) IDENTIFY YOUR TARGET BEYOND ALL DOUBT
5) CHECK YOUR FIRING ZONE
6) STORE FIREARMS AND AMMUNITION SAFELY
7) AVOID ALCOHOL AND DRUGS WHEN HANDLING FIREARMS