In a speech on Wednesday, Mr Dutton compared the response to the protest - which took place just days after the outbreak of violence in the Middle East - to the mass shooting in Tasmania where 35 people were killed.
"While no one was killed during the October 9 protests, the events at the Sydney Opera House were akin to a Port Arthur moment in terms of their social significance," Mr Dutton said in the speech.
But the comments have attracted condemnation.
Jeremy Rockliff has taken federal Liberal leader Peter Dutton to task for commenting on Port Arthur. (Rob Blakers/AAP PHOTOS)
Mr Rockliff, a Liberal premier, said such a comparison to should not have been made to the massacre.
"It is never appropriate to compare the Port Arthur tragedy with anything, in any circumstance. This is still raw for many Tasmanians and will be forever raw with those who are directly affected," he told ABC Radio.
"It's up to Mr Dutton in terms of clarifying what he has said.
"My view is we need to be very careful and never compare the Port Arthur tragedy to anything but the absolutely tragedy that it was."
Federal Liberal MP Bridget Archer, who is also from Tasmania, said the opposition leader's comments were disrespectful.
"(The comments were) incredibly disrespectful to the victims and survivors of one of the darkest days in our nation's history and a wholly inappropriate and somewhat bizarre comparison," she said.
But Mr Dutton has stood firm, saying the comparison was a commentary on the prime minister's leadership.
"The point I was making - which is absolutely a legitimate one - is that I thought this was a time for the prime minister to show leadership and to step up," he told Nine's Today program on Friday.
"You've got a contrast with John Howard, who stood up at a point of national importance for our country, demonstrated leadership and changed the course of history for the better."
Thirty five people were killed and 28 wounded at Port Arthur on April 28, 1996. (Rob Blakers/AAP PHOTOS)
Following Port Arthur massacre, the then Liberal prime minister introduced sweeping gun control legislation.
While acknowledging criticism about his reference to Australia's worst mass shooting, Mr Dutton doubled down.
Prime Minister Anthony Albanese had failed to act to reduce anti-Semitism in the community in the wake of the Gaza conflict, he said.
Government Services Minister Bill Shorten said while it was important to call out prejudice, the comparison to Port Arthur was wrong.
"I agree that some Jewish people do feel unsafe in this country for the first time, it needs to be called out, but I think the one thing Mr Dutton has made a mistake about ... is conflating it with Port Arthur," he told Today.
But deputy opposition leader Sussan Ley said anti-Semitism needed to be called out.
"The point Peter Dutton was making (was) there are pivotal and seminal moments in our nation's history where prime ministers need to stand up," she told Sunrise.
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