John Howard, who introduced national gun control laws 20 years ago after the Port Arthur massacre, says the existing laws are inadequate and should be tightened.

Speaking on SBS’s Insight program to Alpha Cheng, the son of NSW police employee Curtis Cheng who was fatally shot in Parramatta last year, the former prime minister said “almost certainly … the laws are not adequate” and he would “encourage sensible strengthening of the existing laws”.

“I would have thought that everybody would agree, if 15-year-olds can get hold of weapons like that, there is something wrong with the laws,” Howard told the audience of Insight’s episode on guns, which airs on Tuesday night.

“I’m not going to preach at the state government over this – they have to make a judgment about it. But I’m wholly against any watering down of the existing laws, and I would encourage sensible strengthening of the existing laws,” the former Liberal prime minister said.

The 20th anniversary of the Port Arthur massacre, when Martin Bryant killed 35 people in Tasmania, is this month. Howard overcame opposition to quickly introduce a sweeping package of restrictions on gun ownership. There have been attempts to roll back some of the measures in some states.

“Once you give people access to weapons and those people snap [or] exhibit a mental illness, then you will have tragedy,” he said.

Howard said he does not object to another firearms amnesty, but he has not been actively campaigning for one. “I think they work better if they are done nationally,” he said.

Cheng, 58, was gunned down outside Parramatta police station on 2 October, 2015, by 15-year-old schoolboy shooter Farhad Jabar, who was later fatally shot by police.