Extremists have targeted two women MPs in Sydney with rape and death threats after they criticised a weekend neo-Nazi rally that police concede was not the right-wing extremist’s first approved gathering.

Federal MP Allegra Spender and state MP Kellie Sloane, whose overlapping electorates in eastern Sydney have large Jewish populations, have referred to police several inflammatory threats directed towards them on Sunday.

The threats followed both women condemning 60 black-clad men shouting Nazi slogans and unfurling a large banner across the gates of NSW parliament on Saturday, carrying the slogan: “Abolish the Jewish Lobby.”

The men were linked to the National Socialist Network.

A leader of one neo-Nazi group urged his “patriots” to “rhetorically rape Allegra Spender”, triggering hundreds of messages aimed at the independent MP.

“It is pretty shocking and not something you ever want to hear, but we’ve referred it to the police,” Spender told ABC radio on Monday.

“These are the real extremists out there. They’re trying to intimidate the broader mainstream community.”

She criticised police and the government for allowing the rally to go ahead.

“It’s very unclear so far, from the NSW government and also the NSW police, what should have happened instead of what actually did happen,” Spender said.

Barely six weeks into his new job, NSW Police Commissioner Mal Lanyon vowed to get to the bottom of a command-level decision to not oppose Saturday’s gathering in central Sydney.

Organisers gave notice more than a week earlier and got the green light because police flagged no public safety concerns, Lanyon said.

That followed the force seeking advice on legal options about how a court challenge would fare.

“This group had protested before … we’ve also had interactions with them,” Lanyon said.

“There had been no issue with public safety in those particular ones.

“We sought legal advice in terms of the content of what was in the banner that was to be used and we were told that there was no reasonable prospect of prosecuting on that.”

The fringe group also rallied outside the NSW parliament in June, when participants wore black uniforms and displayed a banner with the words: “End immigration.”

Brushing off suggestions some police officers were empathetic to neo-Nazi messages, Laynon said he found the group and its rhetoric odious.

NSW Premier Chris Minns condemned the “vile” and “bigoted” abuse towards Spender and Sloane, and vowed action on the rally itself.

“I’ll be reviewing the speeches to determine whether existing hate speech laws have been breached or not,” he said.

“We can’t let this happen again.”

Minns dismissed suggestions of a double standard in how police curbed protests by climate and pro-Palestine groups compared with those from neo-Nazi extremists.

Sloane, whose state electorate of Vaucluse is home to 15 per cent of Australia’s Jewish population, said the government’s handling of the rally was a “complete stuff-up”.

She remained defiant in the face of the violent threats, which prompted her to deactivate her X account.

“I won’t be intimidated by them and I won’t stop speaking up about behaviour that is racist and offends the majority of decent people in NSW,” she said.

-AAP