Support for One Nation has risen four points to 31%, a Redbridge Group/Accent Research poll, published on Monday by The Australian Financial Review, shows.
Labor's primary vote is at 28%, down three points since the poll firm's last survey a month ago and the government's budget that was announced on May 12. The coalition dropped two points to 20%.
One Nation MP Barnaby Joyce said the poll was an "indicator, not a vote" and said the right-wing party wasn't getting ahead of itself.
"That would be hubris. It's an incredible honour," he told Seven's Sunrise programme on Monday.
Support for the Greens dipped one point to 12% and backing for the "other" category of parties rose two points to nine percent.
Labor leads One Nation 51% to 49% 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% 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: the prime minister 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, with 31% favouring the Labor leader, while Senator Hanson is on 25% and Mr Taylor on 14%.
Mr Albanese's lead on the measure dropped two points and Senator Hanson's rose by two points while Mr Taylor's remained unchanged.
Senior Labor minister Tanya Plibersek said One Nation needed to begin providing more detailed policies if it wanted to form government.
"This is really typical of One Nation. You get a long list of complaints and no solutions," she told Sunrise.
Mr Joyce said he would start with repealing large parts of Labor's budget and scrapping the climate change department.
New Liberal party president and former prime minister Tony Abbott said he wouldn't disparage Senator Hanson because she had shown a lot of resilience over the years.
"But I do believe that the strong Liberal-National coalition has proven again and again that we are capable of giving Australia the good government our country so desperately needs," he told Nine's Today Show.
Before the poll results were released, Senator Hanson told Sky News on Sunday she has what it takes to become prime minister, but added she wasn't sure if she would ever achieve the role.
She also expressed confidence One Nation MPs would be able to form a competent cabinet if her party won government.
The poll said 63% 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.
