Federal police are investigating a Melbourne protest where Hezbollah flags were displayed in what shapes as an early test of hate-symbol laws passed late last year.

It comes as Immigration Minister Tony Burke told the ABC on Tuesday he had asked police to make him aware of any non-citizens caught up in investigations so he could cancel their visas, saying visitors would fail their character test if they were "inciting discord".

"We don't know whether they are actually on visas … [but] we do have a higher standard if you're on a visa," he said.

"The normal principles that might be there where people will have arguments about freedom of speech — when you're a guest in someone's country, you're there as a guest."

AFP Deputy Commissioner Krissy Barrett said the investigations were to determine whether the flags displayed at the protest, which called for ceasefires in Gaza and Lebanon, violated laws prohibiting the display of hate symbols.

Those laws were passed in January primarily in response to the display of Nazi symbols, but they also cover the symbols of listed terrorist organisations such as Hezbollah.

Deputy Commissioner Barrett said the law laid out several conditions which would need to be met to secure a conviction, and these had not been tested in court.

"[It's] not just merely the display of the symbol; there are a number of elements that need to go alongside the display," she said.

"It's got to be done in circumstances in which a reasonable person would consider that the conduct either advocates inciting others to use violence or use force [or] could incite others to humiliate or intimidate based on religion …

"The context around the conduct is extremely important … If they're holding the flag, what are they saying? What are they chanting? What are they wearing? What sort of physical behaviour are they demonstrating?"

She added the AFP had been in contact with NSW Police over protests in Sydney but had not commenced any of its own investigations over that protest.

"Legislation is available to our state and territory colleagues as well, so it is the case that NSW Police can commence their own investigations."

NSW Police said it had seized two flags allegedly displaying Hezbollah's symbol. The ABC has verified at least one flag with a Hezbollah symbol on it, and some protesters also held photos of Hassan Nasrallah, the Hezbollah leader killed in Israeli strikes last week.

The protests have drawn criticism from Jewish community groups, with Jewish Community Council of Victoria CEO Naomi Levin saying it was "highly disturbing" to see the flag of an organisation that had "perpetrated numerous … murders of Jewish people not just in Israel but around the world".

Islamic Council of Victoria president Adel Salman condemned the use of the flag, which he said was held "an absolute minority of people". He said the protests were "purely about supporting Palestinians".

"These Hezbollah protests are not welcome," he said.

AFP Commissioner Reece Kershaw told Nine radio on Tuesday the AFP was "taking action and we'll use the full force of the law as it applies to these offences …"

"My view is it's un-Australian, it's against the law and it's not in accordance with our values," he said.

"So the fact that we have met the threshold of publicly displaying prohibited terrorist organisation symbols, we'll be taking action."

Dutton and Burke trade barbs over government response

Opposition Leader Peter Dutton said it was the federal government's job to direct police how to enforce the laws.

"The direction ultimately is taken from the prime minister and the minister, and if the minister is saying to the [AFP] commissioner we don't want to see arrests, or we're just happy if you enforce – you know, keep the peace but not enforce the law, that needs to be made publicly known."

There is no suggestion any minister has directed the AFP not to enforce any law. And while the AFP can lay charges, convictions are a matter for courts.

Mr Burke said the laws were "the strongest statement on hate speech that the parliament has ever taken" but would "have to be tested before the courts".

Mr Dutton said parliament should be recalled if stronger laws were needed, which Mr Burke branded a political ploy.

"With Peter Dutton it is always about the Middle East and never about middle Australia … If you wanted to recall the parliament, you'd do it on the cost of living," he said.

"These are laws that Peter Dutton supported when they were passed a year ago."

Attorney-General Mark Dreyfus told the ABC the government had "faith in our police forces to enforce the law".

"In a democracy like ours, it is entirely inappropriate to suggest the Australian Federal Police should be arresting people at the direction of politicians," he said.

"Any person who shows support for terrorist organisations, including by displaying symbols used by terrorist organisations, are of active interest to ASIO."

Mr Dutton also said Mr Burke should already have cancelled some visas.

"He keeps talking about it but he doesn't do it, and that's why people continue to act out," he said.

Mr Burke declined to say whether waving a Hezbollah flag would be grounds for cancellation of a visa, saying he did not want to risk appearing to have pre-judged any individual's case in the event a cancellation was challenged in court.

"[But] I've got very strong views against hate speech and hate symbols, and I don't want the anger and hatred from around the world being imported into Australia," he said.

Mr Burke added he was "surprised" by the focus on visa holders. 

"We've had protests like this before and [authorities] haven't come back with anyone on visas," he said.

Dutton says Islamic community not facing terrorist threat

The federal government appointed Aftab Malik as its Islamophobia envoy on Monday, more than two months after it appointed Gillian Seagal as an anti-Semitism envoy.

Mr Burke said "finding the right person [had] taken a while" but both positions were "particularly important" to combating religious-based discrimination because there were not currently legal protections against religiously motivated hate speech as there were for race.

The government introduced laws to parliament in September which would outlaw speech that incited violence on the basis of religion, among other characteristics.

"If you go to the person most likely to be targeted for abuse in Australia right now, it's an Islamic woman wearing a hijab. I don't want that to be the case," Mr Burke said.

Mr Dutton said he was "happy for there to be an envoy" but that he did not believe Islamophobia was a comparable threat to anti-Semitism.

"What we're seeing in our country at the moment is not levels of Islamophobia that are where the anti-Semitism is at," he said.

"The schools with armed guards are not the Muslim schools, they're the Jewish schools … The threat of a terrorist attack and people being discriminated against at the moment are against the Jewish community and not against people within the Islamic community."

The Islamophobia Register of Australia and the Executive Council of Australian Jewry track reported incidents of Islamophobia and anti-Semitism, respectively, using different methodologies.

Each group published a preliminary report focused on the immediate aftermath of the October 7 attack last year and reported that incidents of hatred had spiked significantly.

"We always need to remember, while it hasn't happened here in Australia, the Christchurch massacre was conducted by an Australian," Mr Burke said.

"Islamophobia can lead to forms of terrorism and violent extremism that are absolutely horrific."

In August, intelligence chief Mike Burgess upgraded the national terrorism threat level from possible to probable and emphasised there was no one category of threat, also warning politicians against statements likely to inflame domestic tension.