“People have to know that they are carrying a symbol that is prohibited. Generally speaking, we give them the opportunity to remove that symbol, and if they don’t, and they continue presenting that symbol in a public place, then they may have committed that offence,” Assistant Commissioner Peter McKenna said.

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Several Sydney mosques are holding memorial services for former Hezbollah leader Hassan Nasrallah after he was killed in an Israeli airstrike on Beirut. At least three mosques across the city have advertised memorial services for Hassan, who led the powerful militant group from 1992 until his death at the weekend.

It has been a federal offence since January this year to display the symbol of a terrorist organisation in public, after laws were passed to crack down on the display of Nazi swastikas, ISIS flags and other symbols of prohibited groups.

The deaths of the Lebanese Shia militia leader and several of his top lieutenants have upended the Middle East war and inflamed the already heated domestic debate over Israel’s military response to Hamas and Hezbollah.

After months of searching for a community leader willing to be the envoy to combat Islamophobia, the Albanese government has announced that Aftab Malik, a British scholar and anti-extremism expert, will take on the role.

Malik said fighting against hate in Australia was more important than ever and that “antisemitism and Islamophobia are not mutually exclusive: where there is one, you most likely will find the other lurking”.

Federal and state government sources said there was little enthusiasm from state police to enforce untested federal laws on extremist rhetoric and motivation. An AFP spokesman stressed the federal police do not “routinely attend protests as this is the primary responsibility of state and territory law enforcement”.

Political pressure on the police to act built throughout Monday as Prime Minister Anthony Albanese said: “Our multiculturalism and social cohesion cannot be taken for granted, and it’s important that we continue to stress that that is the case as we go forward as well.”

Coalition leader Peter Dutton said it was “unacceptable that the government wouldn’t be arresting people already”, adding that terrorist sympathisers had “no place in our country”.

Victorian premier Jacinta Allan said she expected police to pursue protesters, adding: “This is driving deep grief and division here on the streets of Melbourne.”

Liberal Senator Dave Sharma, a former Australian ambassador to Israel, said on Sky News he didn’t see “how any Jewish person could feel safe in Sydney or Melbourne’s CBD on Sunday”.

The chants heard at the Melbourne rally refer to the historic battle of Khaybar in which Jews were massacred. The Khaybar chant has been used at pro-Palestinian protests around the world for years and Jewish groups consider it to be antisemitic.

The Hezbollah flag was brandished by protesters in both Melbourne and Sydney.

John Coyne, head of policing at the Australian Strategic Policy Institute, said the freedom to protest was fundamental in a democracy. But terrorist insignia such as flags were deemed beyond the pale, just as the Nazi swastika is also a banned symbol.

Some people who used Hamas and Hezbollah symbols were probably ignorant of the group’s motivations, he said, and authorities should only seek prosecutions if an individual had violent or extremist intent.

He questioned the legality and morality of Israel’s military campaign but argued protesters should not align themselves with violent movements whose charters called for the extinction of Israel.

“You can actually be nuanced,” he said.

A spokesperson for the Greens said the protest organisers were not associated with “the small group of people waving flags”, without referencing Hezbollah or condemning support for extremist groups.

Melbourne rally organiser Omar Hassan said a mass protest movement was bound to have diverse views but the presence of a small number of Hezbollah symbols at a rally should not divert attention from Israel’s actions in Gaza and Lebanon.

“I think the media focus on this small group of protesters is a distraction from the war crimes that Israel is committing in Lebanon, and it’s a deliberate distraction by supporters of Israel and the Liberal Party,” said Hassan, a member of the Victorian Socialists political party.

When asked about the chants, Hassan said protest organisers disavowed any message that framed the conflict in Palestine as a struggle between Jews and Muslims.

With Broede Carmody

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