Prime Minister John Key says he would be reluctant to see police carry guns all the time because it would raise a barrier between them and the public.
The Napier siege has reignited the issue and Mr Key said at his post-Cabinet press conference yesterday it was a legitimate debate.
Arming the police would create substantial risks, he said, citing international evidence that the weapons were often used against the police themselves.
"And the weapons need to be loaded at all times.
"There's likely to be a psychological barrier between the police and the public," Mr Key said.
He said the rollout of Taser stun-guns would be brought forward and an announcement on that would be made in the budget on May 28.
He would not go into details.
Mr Key earlier praised the police for the way they handled the stand-off with Napier gunman Jan Molenaar.
On Thursday, Molenaar (51) shot dead Senior Constable Len Snee and wounded two other policemen and a civilian.
Mr Key, speaking on Radio Live, said stories of heroism were yet to be told.
"There were some really heroic acts.
"I understand police officers actually threw themselves [to] cover the bodies of the two injured police officers.
"I don't know all the stories yet.
"It's a terrible situation, but I think there are going to be some great stories of heroism."
Mr Key said he intended going to Snr Const Snee's funeral tomorrow - to be held in the Napier Municipal Theatre at 1pm - with Cabinet colleagues, including Police Minister Judith Collins and Maori Affairs Minister Pita Sharples.
Police had dealt with the tense situation well, he said.
"I think they did a very, very good job.
"It was an extremely difficult circumstance.
"No-one really knew if the house was booby-trapped, what weapons he had.
"They just knew that he was unstable, dangerous and had killed," Mr Key said.
He said the case had raised concerns about the number of unregistered weapons in New Zealand but emphasised the case was not a common occurrence.
Police said yesterday two of the three bullets that hit Snr Const Snee were not survivable.
He was hit in an arm and the upper and lower torso, police told a press conference.
Either shot to the torso would have proved fatal, and death would have been instantaneous, Superintendent Rod Drew said.
Fragments of a .223 calibre bullet were found in his body.
Police would still not reveal how Molenaar died.
Supt Drew said Molenaar was found dead in the main bedroom of his house on Saturday following sporadic contact by phone with police negotiators the day before.
Early on Friday afternoon, Molenaar told his partner, Delwyn Keefe, he did not want to come out, did not want to go to jail for killing Mr Snee and "would do it his way".
A short time later, he sent a text to a close family member and five minutes later a single shot was heard from inside the house.
It should not be concluded Molenaar took his own life, Supt Drew said.
The two injured officers and the civilian, shot at the start of the siege on Thursday morning, were said to be improving slowly.
Snr Const Bruce Miller and civilian Leonard Holmwood were still in the intensive care unit of Hawkes Bay Hospital, in drug-induced comas.
