Federal police say they have “received reports of a crime” in relation to comments made to the media by Pauline Hanson this week.

But an AFP spokesperson did not say whether they had begun a criminal investigation, only that they would have more to say “at an appropriate time”.

Bilal El-Hayek, the mayor of Canterbury Bankstown in western Sydney, said on Friday that the One Nation leader should face charges over her “highly inflammatory” comments about Muslims.

In El-Hayek’s council area more than 23% of residents are Muslim, according to the 2021 census. He told the ABC on Friday that hate speech laws were “quite clear” with a reference to public incitement of hatred and violence.

On Monday night, discussing the thwarted attempts by Australian women and children stuck in Syria to return home, Hanson said on Sky News: “You say, ‘Well, there’s good Muslims out there.’ How can you tell me there are good Muslims?”

Hanson has not withdrawn the comments, though she has offered some further comments framed as a conditional apology. In one of the subsequent interviews she also singled out Lakemba, a suburb within Canterbury Bankstown, as somewhere people “feel unwanted” and do “not want to be”.

El-Hayek said that “[Hanson’s] target was clearly the Muslim people”.

“I have no doubt that her remarks will incite someone,” he said.

One of Australia’s largest mosques – Lakemba – on Wednesday received its third threatening letter in a matter of weeks, ahead of the first night of prayers in Islam’s holiest month. NSW police are investigating the incident while a man has been charged over a letter sent to the mosque in January.

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Asked whether they were investigating the comments by Hanson, a spokesperson for the Australian federal police said “the AFP is aware of comments made during a media interview earlier this week”.

“The AFP has received reports of crime in relation to this matter. Further comment will be made at an appropriate time.”

Prof Simon Rice, a University of Sydney law expert, said alleged hate speech can be prosecuted in any jurisdiction where the comments have been broadcasted.

Under NSW, it is a criminal offence to publicly threaten or incite violence towards a person or group of people on numerous grounds, including people’s religious belief and affiliation. Under the state’s new laws, which came into effect last year, it is also an offence to publicly incite hatred on the grounds of race.

Rice said Hanson could be investigated under the NSW laws however these alleged offences are “very difficult to prove”.

“The mayor is right to call for… police to look at it, whether they [lay a] charge is a different question altogether,” he said.

He said people could also take civil recourse by lodging a complaint under the federal anti-discrimination laws or state legislation. He pointed to Greens senator Mehreen Faruqi’s successful racial discrimination case against Hanson.

The One Nation leader’s comments this week have been widely criticised. Hanson’s One Nation colleague Barnaby Joyce refused to endorse them on Wednesday.

The federal opposition leader, Angus Taylor, said on Friday he did not agree with Hanson’s recent remarks about Muslims.

“I’ll always distance myself from people who think this is about anything other than protecting our life and focusing on our core values,” he told reporters.

“If people want to come to our country, no matter [their] religion, [if] they don’t believe what we believe then we should shut the door on them.”

Taylor was visiting Melbourne’s Addas synagogue, which was firebombed in an 2024 antisemitic attack that the domestic spy agency has linked to Iran. Asked if Hanson should apologise for her comments, the new opposition leader said it was a matter for the One Nation senator.

The Albanese governments race discrimination commissioner this week called for Hanson to apologise for her comments, saying she was targeting Muslims and her comments would have a lasting impact.

Anthony Albanese this week both drew a link between Hanson’s comments and the potential for threats of violence. The NSW premier, Chris Minns, said Hanson’s comments may have “inflamed tensions”.

On Wednesday, Hanson offered a conditional apology if she “offended anyone out there that doesn’t believe in sharia law, or multiple marriages, or wants to bring ISIS brides in, or people from Gaza that believe in a caliphate”.

Hanson has previously been criticised for demeaning Muslims when she wore a burqa in the Senate chamber last year. She was suspended from the chamber for seven days.

Hanson declined to comment.