Home Affairs Minister Tony Burke introduced the bill to parliament on Tuesday, after emotional condolence motions were delivered the day before to honour the 15 victims of the December 14 terror attack.
The government will try to pass two bills focused on gun reform and hate speech.
The legislation was originally proposed as a single omnibus bill, but the government was forced to split it after opposition from the coalition and the Greens on anti-vilification laws.
The gun laws propose to tighten licensing rules and expand intelligence checks, while the coalition labelled the bill as flawed.
Beginning the debate, Mr Burke said the two father-and-son gunmen had "hate in their hearts and guns in their hands" and the government must do all it can to combat the motivation and method of the massacre.
"A critical question I've often been asked during this debate is, if this national reform package had already been in place, how many firearms would the Bondi gunmen have held?," he said.
"The answer is zero."
Under the reforms, the father would have been ineligible because he was not a Australian citizen, he said.
"And the son who didn't have a firearms licence, in any event, had he tried any intelligence holdings with respect to him, would have formed part of the licensing decisions," Mr Burke added.
Nationals leader David Littleproud, who immediately opposed the changes, fired up as he called the gun bill a "cheap political diversion" from religious extremism.
"We do not have a gun problem, we have a radical Islam problem," he said.
He said his party supported a national gun register and the provision enabling firearms background checks, but said the bill went too far overall.
"What they are trying to do is demonise gun owners for a cause that did not take place because of them," Mr Littleproud said.
Not all regional MPs were against the bill.
Independent Helen Haines, who represents the regional Victorian seat of Indi, backed the reforms, calling them "common sense".
They do not target farmers, sporting shooters or other law-abiding gun owners, she added.
"They are about making sure people who pose a real risk - including violent extremists and individuals on an ASIO watchlist - cannot legally access firearms," she said.
Shadow attorney-general Andrew Wallace lashed the national buyback scheme, which would incentivise gun owners to hand their firearms in for payment.
The Queensland government said it would not be participating in the scheme, the cabinet agreed on Monday night.
The Northern Territory government has also rejected the co-funding proposal, while Tasmanian government has not settled on a position.
"The 1996 buyback (implemented by John Howard) was properly funded ... this buyback calls on the states and territories to foot half the bill, irrespective of their capacity to pay," Mr Wallace said.
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