During Tuesday's debate, Nash recalled the regret of former Police Minister John Banks over not banning "killing machines" after the 1990 Aramoana massacre.
"I don't want to be that Minister in 20 years' time, expressing my regret that the gun lobby won out," Nash said.
"We owe it to police, and we owe it to the victims and the survivors of the mosque terror attacks to make these changes. "
Other major changes in the bill include new licensing rules for gun clubs and significantly stricter penalties for breaches.
For example, the legislation will increase the maximum penalty for having a gun with a licence from a maximum $1000 fine and three months' jail to $15,000 and a year of prison.
But National's Brett Hudson said the Government was "delivering something other than what it says on the tin".
The Opposition this week laid out what it said was a list of 13 changes it wanted to see before backing the bill, including more flexible firearm rules for gun and sports clubs.
"It isn't focused on criminals at all. In fact, it has it, in our view, 180 degrees the wrong way around, Hudson told the House on Tuesday.
"Instead, the bill is imposing greater regulation, more responsibilities and more costs on law-abiding New Zealand who happen to own firearms and is doing anything of any little any substance to address criminal activity and particularly gangs."
Earlier in the day, Prime Minister Jacinda Ardern said United States President Donald Trump had expressed interest in New Zealand's first tranche of gun reforms when the pair met in New York.
Trump is understood to have asked Ardern, unprompted, about the gun law reform that she pushed through in the aftermath of March 15, which banned most military-style semi-automatic firearms and led to a buyback process that so far has collected about 20,000 firearms and paid out $36.7 million.
"We were able to move quickly and with consensus, and that obviously stood out to the world... he listened with interest," Ardern said.
"I certainly wouldn't want to predetermine that means anything in particular for the US other than an interest in what we did."