A Redbridge Group/Accent Research poll, published on Monday by The Australian Financial Review, shows support for One Nation has risen four points to 31 per cent.
Labor's primary vote is at 28 per cent, down three points since the poll firm's last survey a month ago and the government's budget that was announced on May 12, and the coalition dropped two points to 20 per cent.
Support for the Greens dipped one point to 12 per cent and backing for the "other" category of parties rose two points to nine per cent.
Labor leads One Nation 51 per cent to 49 per cent on the Redbridge poll's two-party-preferred basis, calculated by asking respondents how they would direct their preferences.
The poll of 1005 voters was conducted between Monday and Thursday, and has a 3.4 per cent margin of error.
The poll shows Senator Hanson's net favourability - her approval rating minus her disapproval rating - at zero.
No Australian politician in the poll has a positive net favourability rating: Prime Minister Anthony Albanese is on minus 19 while both Liberal leader Angus Taylor and Nationals leader Matt Canavan are on minus four.
Mr Albanese remains the preferred prime minister in the poll, with 31 per cent favouring the Labor leader while Senator Hanson is on 25 per cent and Mr Taylor is on 14 per cent.
Mr Albanese's lead on the measure dropped two points and Senator Hanson's rose by two points while Mr Taylor's remained unchanged.Â
Before the poll results were released, Senator Hanson told Sky News on Sunday she had confidence One Nation MPs would be able to form a competent cabinet if her party won government.
"I'm getting a great team around me, and even those members of parliament that I have now, they're great, down-to-earth - the experience and knowledge they have behind them, it's marvellous," Senator Hanson said.
Senator Hanson again said she was considering moving to the lower house at the next election but she did not say which seat she wanted to contest.
"I'm not making a decision now and I'm not going to tell anyone what I'm doing at this moment because I haven't clearly made up my mind," she said.
By convention, Australia's prime minister serves in the lower house rather than the Senate.
The poll said 63 per cent of respondents believed Australia was heading in the wrong direction, a result Redbridge director Tony Barry said helped explain One Nation's surge.
"That pervasive negative mood sentiment is fuelling more anti-establishment support and a view among a growing cohort of voters that the answer lies outside established norms and major parties," Mr Barry said.
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