Bryant used a semi-automatic ArmaLite rifle and a semiautomatic SKS assault weapon to gun down his victims.
Mr Howard said Australia's gun lobby was not as powerful or as well financed as the National Rifle Association in the US, but that he'd faced resistance from some states and from the coalition's rural constituents.
He wore a bulletproof vest while addressing farmers in rural Victoria and faced angry gun owners as he garnered support for the reforms.
A federally financed gun buyback scheme was needed to make the plan work, he said.
"This required new legislation and was widely accepted across the political spectrum," Mr Howard wrote.
"Almost 700,000 guns were bought back and destroyed - the equivalent of 40 million guns in the United States."
The ready availability of high-powered weapons, which enabled people to convert "murderous impulses into mass killing", was the fundamental problem, Mr Howard said.
"Certainly, shortcomings in treating mental illness and the harmful influence of violent video games and movies may have played a role," he wrote.
"But nothing trumps easy access to a gun.
"It is easier to kill 10 people with a gun than with a knife."
Mr Howard said the coalition government had been willing to hold a nationwide referendum to change the constitution and give the federal government constitutional power over guns.
"Such a referendum would have been expensive and divisive, but it would have passed," he said.
"And all state governments knew this."
The battle to reform gun laws was won because there was majority support across the nation for a ban on certain weapons.
"And today, there is a wide consensus that our 1996 reforms not only reduced the gun-related homicide rate, but also the suicide rate," he said.
"The Australian Institute of Criminology found that gun-related murders and suicides fell sharply after 1996."
The gun buyback scheme was credited with reducing the number of firearm suicides by 74 per cent.
Before the 1996 reforms Australia had experienced 13 gun massacres resulting in a total 102 deaths.
"There has not been a single massacre in that category since 1996," Mr Howard said.
"Few Australians would deny that their country is safer today as a consequence of gun control."
- AAP