Peter Dutton has called for the deportation of temporary visa holders who attend pro-Palestinian rallies as Australia's domestic spy agency warns "words matter" and can inflame community tensions.
The fallout continues after video was beamed around the world of anti-Jewish chants being shouted on the steps of the Sydney Opera House while it was lit up in the colours of the Israeli flag.
Mr Dutton said non-citizens who preached anti-Semitic speech at the rallies should be deported.
"People with that hate in their minds, in their hearts, don't have any place in our society," the Opposition Leader told Sydney radio 2GB.
"If they were non-citizens, their visas should be before the minister and on character grounds they should have their visas cancelled."
But rally organiser Palestinian Action Group Sydney, which previously denounced the chants made by a small group on Monday night, called Mr Dutton's comments "a shocking attack on democratic rights".
"People have a right to protest against the war crimes and apartheid policies of the Israeli state," the group said.
Islamist group Hamas on Saturday launched attacks on Israeli towns that killed more than 1200 people, with scores of others taken hostage after militants breached a fence enclosing Gaza.
Israeli reprisal strikes on blockaded Gaza have reportedly killed 1100 people.
The head of Australia's domestic spy agency ASIO said protests would continue and are "likely to feature strong emotive claims".
"I remain concerned about the potential for opportunistic violence with little or no warning," director-general Mike Burgess said on Thursday.
Mr Burgess cautioned "words matter", noting the agency "has seen direct connections between inflamed language and inflamed community tensions".
Home Affairs Minister Clare O'Neil urged Australians to consider the optics of rallies that could further hurt an already reeling Jewish community, adding it was not about political views on Israel and Palestine.
"What has happened here is a terrorist organisation has indiscriminately attacked and killed innocent men, women and children," she told ABC TV.
Organisers will push ahead with a second Sydney rally on Sunday despite a lack of police approval to march on the streets, but they have moved it from Town Hall to Hyde Park.
"This will be a static rally, we will not march but we will be loud, we will be proud and we will show the state that we are in full support of the Palestinian people and will not bow down to their attempts to silence our movement," they said.
Australian Palestine Advocacy Network president Nasser Mashni said what happened on Monday was unacceptable but he defended the group's right to protest.
"The reality of people coming together to express concerns about situations is that, at times, unwanted people come along and provoke unnecessary and unwanted actions," he said.
"Violence is never going to be an answer, as anti-Semitism is never the answer."
The Australian Muslim Advocacy Network called on Mr Dutton and Prime Minister Anthony Albanese to consider the impact of their language around the Israel-Palestine crisis.
"Australian leaders must take responsibility for the effects of their actions on civilians under occupation, in war overseas and Australians at home," the network said.
"The detrimental effects for health, wellbeing and safety are significant and ongoing."
Pro-Palestine rally organisers plan to hold gatherings across Australia with protests in Canberra, Perth and Brisbane on Friday.
Events will also be held in Melbourne, Sydney and Adelaide on Sunday.
South Australian Premier Peter Malinauskas said people were free to protests lawfully.
"In South Australia, there is an absolute right for people to be able to express their political views freely in the form of protest," he said on Thursday.
"But we've got a very firm view as a government that we will not be tolerating any acts at the protests that are contrary to the law."
Brisbane Lord Mayor Adrian Schrinner said he was concerned by rising anti-Semitism in the community.