Vigils following the death of Iranian supreme leader Ayatollah Ali Khamenei have been slammed as "completely at odds" with Australian values.
Prime Minister Anthony Albanese is among those criticising a small group of Shia mosques and Islamic centres in Sydney and Melbourne that invited members to mourn the cleric.
The 86-year-old was killed in early strikes on Iran launched by the US and Israel.
Opposition frontbencher Andrew Hastie described Khamenei as an "evil man".
"Anyone who's celebrating the Ayatollah is celebrating a form of militant political Islam, which is completely at odds with our values here in Australia, our way of life," he told Nine's Today program on Tuesday.
"If people are displaying the symbols of a listed terrorist organisation, or indeed glorifying it, they should be looked at by police."
Mr Albanese said it was inappropriate for events mourning the leader to go ahead.
"Overwhelmingly, people won't be participating," he told ABC's 7.30 program.
The supreme leader's death was celebrated by many members of the Iranian community in Australia on Sunday at snap rallies held in major cities.
Asked if police should investigate mosques that invited people to mourn the death, Defence Minister Richard Marles said he was not going to suggest what action law enforcement should take.
"Our thoughts are with the thousands of Iranians who have died at the hands of the supreme leader just in the last few weeks," he told Today.
"This is an oppressive autocracy which has oppressed its own people, and we stand with the Iranian people, and that's where people's thoughts should rightly be focused today."
NSW Premier Chris Minns warned people planning to hold events they might fall foul of the law.
"It's atrocious to use an opportunity to commemorate or memorialise an evil person," he said.
"Anybody that's holding these commemorations need to be very careful that they're not breaching hate speech or terrorism laws in the state because they can expect it to be investigated in those circumstances."
Israel's ambassador to Australia, Hillel Newman, said people celebrating the attacks on Iran were on the "right side of history".
"Those that mourn the death of a rogue, brutal regime, a leader of this regime who was a mega terrorist, they've lost their moral compass," he told reporters in Canberra.
