Anthony Albanese has linked comments by Pauline Hanson about Muslims to a heightened risk of violence as one of his cabinet ministers warned Liberals against chasing One Nation on immigration, saying “you can’t out-racist Pauline Hanson”.

Police are investigating a series of threats received by Lakemba Mosque in Sydney as the holy month of Ramadan begins – including a call to kill worshippers – which came days after Hanson said there were no “good Muslims”.

Amid mounting criticism of the comments, the prime minister was asked if there was a link between Hanson’s comments and threats of violence.

“Of course there is, because it legitimises it, it mainstreams it,” he told ABC radio.

“Pauline Hanson is a divisive figure. She’s made a political career out of seeking to divide Australians against each other. And what we need is more unity, not more division.”

He said the country needed optimism and a serious, positive policy agenda and “Pauline Hanson does not do that”.

The education minister, Jason Clare, called the comments “disgusting but not surprising”.

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“I guess my message to the Liberal party is: don’t follow Pauline Hanson down this racist rabbit hole, because you can’t out‑racist Pauline Hanson, and if you do, you’re only going to end up hurting yourself.”

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

Later, Hanson qualified some of the comments, offering 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’s comments have been roundly criticised, with even Hanson’s One Nation colleague Barnaby Joyce refusing to endorse them on Wednesday.

She also claimed people did not want to visit Lakemba, in Sydney’s south west, claiming “you feel unwanted”.

As many as 5,000 people are expected to attend the mosque each night during Ramadan, swelling to 50,000 on the final day of Eid. NSW police officers are patrolling the site.

ACT independent David Pocock said the “blanket racism” both harms Australia and “sucks the oxygen out of other important conversations”.

“It won’t drive down the cost of living or help with health, ageing, construction, early childhood education or the many other things we should be focusing on to help Australians in their daily lives.”

Maria Kovacic, a Liberal frontbencher, said Australians were “right to be repulsed by those comments, and I don’t equivocate on that.”

The NSW premier, Chris Minns, said an apology was appropriate but he did not expect one to be forthcoming.

“We can’t let the public space be taken over by extremists in these debates, who, let’s be honest, will profit politically by having us divided against one another.

“That is a road some countries have gone down, and we can’t.

“I think we need a big bold open message to people who are normal Australians, to resist this kind of racist ideology and say ‘I’m going to have my fellow Australian’s back’.”

The race discrimination commissioner, Giridharan Sivaraman, said on Wednesday Hanson was targeting Muslims and her comments would have a lasting impact.