Home affairs minister Tony Burke has accused Peter Dutton of seeking to “raise the temperature” of public debate over conflict in the Middle East, after protests on the weekend included some people holding the Hezbollah flag.

The opposition leader on Monday suggested parliament should be recalled to enact new anti-terror laws that would cover such actions, if it was not already illegal.

But Burke rejected Dutton’s demand, saying federal law supported by both parties was already in force, with police and authorities investigating the rallies. He claimed Dutton wanted to “throw more kerosene on the fire” of the public mood around the widening Middle East conflict.

Burke again raised concern about civilian deaths in Lebanon, repeating government calls for a ceasefire as Israel escalated its military operation in the country’s south. But he said the government would not hesitate to cancel visas if those responsible for waving Hezbollah flags at rallies were found to not be Australian citizens.

“I’ve got very strong views against hate speech and hate symbols, very strong views, and I don’t want the anger and hatred from around the world being imported into Australia,” Burke told Radio National on Tuesday.

“With Peter Dutton, it remains the case that no matter how many times our security agencies say we need to lower the temperature in Australia, he wants to raise the temperature every single time.”

The Australian federal police confirmed on Monday that it was expecting at least six reports of alleged crimes from their Victorian counterparts involving symbols and chants which are prohibited under federal hate speech law relating to weekend protests in Melbourne against Israel’s attacks on Lebanon.

Some marchers at capital-city protests over the weekend carried Hezbollah flags and portraits of leader Hassan Nasrallah, who was killed in an Israeli attack.

Hezbollah is proscribed as a listed terrorist organisation under federal law. It is illegal to provide support, to be a member of, or associate with a listed terrorist organisation.

Dutton and the Coalition opposition had demanded visas be cancelled for any non-citizens involved in those actions. Burke yesterday said “any indication of support for a terrorist organisation is unequivocally condemned”.

But the opposition leader claimed the government had not acted swiftly enough.

“To be out there waving a Nazi flag, or a Hezbollah flag, to be out there glorifying a terrorist leader or somebody like Osama bin Laden, it’s completely and utterly unacceptable, and it’s unacceptable that the government isn’t demonstrating the leadership that Australia needs at the moment,” Dutton told Sky News.

“If it continues to compound, if these people know no boundaries, then it will end in tragedy in our country, and that’s something that the prime minister really should be very cognisant of.

“The police and the government need to apply every resource to speak with the leaders in the community, with the imams, etc, to say that these celebrations should not proceed, and there should be very significant pressure applied to the leadership group within the communities to make sure that these celebrations are called off.”

Burke said he was unable to comment directly on the incident, citing potential legal processes, but said he was strongly against “inciting discord and hatred in Australia”, and had asked his department to prepare briefs on whether visas would be cancelled.

The minister said federal law already applied, with current laws supported by both major parties, rubbishing Dutton’s suggestion.

“He doesn’t want to recall parliament because he wants to change laws that he supported a year ago, he wants to recall parliament because he wants to throw more kerosene on the fire and get people angrier with each other and say more outrageous things in the parliament,” Burke claimed.

“That’s what it’s about. It’s nothing to do with Australia.”

Burke said the government did not mourn Nasrallah’s death.

“There are civilians who have been killed who we mourn. There are people who have nothing to do with terrorism, who were alive a week ago and are dead now, and we certainly mourn them,” he said.

“The number of civilians killed is just intolerable, and that’s why the government’s calls for a ceasefire are so important.”

The treasurer, Jim Chalmers, said on Tuesday the government understood that “our communities are hurting” from the growing Middle East conflict.

“We continue to urge restraint and de-escalation, because further hostilities put the lives of tens of thousands of civilians at risk,” he said.

“The global community has been really clear that the destructive cycle in this part of the world must stop.”