New polling shows One Nation edging close to Labor and leading the Coalition, as support grows among older Australians and lower-income voters amid cost-of-living pressures.

Pauline Hanson’s One Nation has become the most popular party among Australian women, according to new polling that also shows the party closing in on Labor’s national vote. A Capital Brief/DemosAU poll released this week put One Nation on 28 per cent, just one point behind Labor on 29 per cent and ahead of the Liberal National Coalition on 21 per cent. In the demographic breakdown, women were the strongest group for One Nation, with 29 per cent saying they would vote for the party, compared with 27 per cent for Labor and 21 per cent for the Coalition. The poll was conducted between February 10 and 20.

The same polling suggests One Nation is also strongest among Australians aged 55-plus, people without a university education, and those earning under $45,000. It performed best in outer metropolitan and regional or rural areas, and was tied for first place with the Coalition among outright homeowners.

On policy areas, respondents most trusted One Nation on immigration, with 33 per cent choosing the party. It narrowly beat the Coalition on housing, but trailed Labor by one point. One Nation fell behind both major parties on cost of living, economic management and energy policy. Cost of living was the dominant issue for voters at 45 per cent, followed by housing at 18 per cent and immigration at 13 per cent.

A separate Sky News Pulse poll released Wednesday, conducted between February 17 and 24, showed the Coalition had lifted its primary vote to 22 per cent, up three points, under new Liberal leader Angus Taylor. In that poll, One Nation was on 24 per cent (down four) and Labor on 29 per cent (down one).

Both surveys come as Hanson was criticised by Labor and the Coalition over remarks about Muslims. The controversy began on February 16 during an interview with Sky News host Sharri Markson, where Hanson said: “I’ve got no time for the radical Islam, their religion concerns me because what it says in the Koran,” and added, “They hate Westerners, and that’s what it’s all about. You say there’s great Muslims out there, well I’m sorry, how can you tell me there are good Muslims?”

Two days later she issued a conditional apology to the ABC, saying she apologised 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”. She then added: “In general, that is what they want — a world caliphate. And I am not going to apologise … I will have my say now before it’s too late.”

The following day, in an interview with ABC TV, Hanson said parts of Australia had become places “people can’t go to” without feeling unsafe, naming Lakemba in Sydney, which has one of the country’s largest Muslim populations.

On Friday, it was reported that Federal Police had received “reports of a crime” relating to Hanson’s comments and were examining the matter. Hanson responded: “They are trying to use Labor’s new hate speech laws to put me back in jail.” Hanson spent 11 weeks in jail in 2003 for electoral fraud, a conviction later overturned on appeal.

Speaking to Sky News on Sunday, Prime Minister Anthony Albanese said he would not speculate about whether the comments could trigger new hate speech laws. “I’m not a lawyer, nor am I in charge of fulfilling those laws. I’ll allow the appropriate authorities to engage,” he said. Albanese also described One Nation as a “political movement that focuses on dividing Australia and pitting Australians against Australians”. “I don’t think they come up with positive solutions. They amplify grievances rather than come up with solutions. And I think that hope and optimism and developing plans for a positive future is what Australia needs.”