A rush on financial shares helped push the ASX above 6,000 points early but the rapid buying has since eased.
The S&P/ASX200 benchmark index was higher by 43.3 points, or 0.73 per cent, at 5984.9 points at 1200 AEST on Thursday.
The All Ordinaries index was 40.6 points, or 0.67 per cent higher, at 6105.5.
Financial stocks gained nearly 3.0 per cent early but had since slipped to be 1.27 per cent higher.
Consumer staples were doing best, up 1.38 per cent, followed by consumer discretionaries, up 1.34 per cent, and health, higher by 1.29 per cent.
Qantas shares rose 6.09 per cent to $4.44 after the carrier said Jetstar would increase the number of flights on domestic and regional routes in June and July.
The airline is operating domestic capacity at just 5.0 per cent of pre-coronavirus level.
Commonwealth Bank was best of the big four after the early rush on financials.
It was up 2.12 per cent to $67.51, while its rivals were more than 1.0 per cent higher.
Westpac investors seemed unmoved by the bank publishing the findings of an investigation into its money laundering and child exploitation scandal.
The report said the failures were due to technology and human error, and not “intentional wrongdoing”.
Goldminer Evolution said it would sell its Cracow mine in Queensland to Aeris Resources for $125 million.
However, traders still kept the Evolution share price down by 1.88 per cent to $5.66.
Among other big goldminers, Northern Star was down 5.88 per cent to $13.45 and Newcrest slipped 2.42 per cent to $29.29.
Among other miners, BHP rose 0.03 per cent to $36.35, Rio was up 1.40 per cent to $98.78 and Fortescue gained 0.41 per cent to $14.72.
In property, developer Unibail-Rodamco-Westfield was one of those that contributed to gains of 1.23 per cent in the sector.
Its price surged by 14.69 per cent to $5.62.
Dexus had a 2.16 per cent gain to $9.46 after completing its 50 per cent acquisition of Rialto Towers in Melbourne.
Elsewhere, Australia’s fourth-biggest mobile service provider Amaysim continued a good run this week and was higher by 21.43 per cent to 51 cents.
The telco on Wednesday bought OVO Mobile and its price was as high as 67 cents earlier in the day.
Meanwhile, the federal government has announced a $688 million HomeBuilder scheme that should help companies in residential construction.
The scheme will offer grants to people who sign contracts to build or renovate their home until the end of the year.
In the US, a survey from payroll processor ADP said that private employers cut nearly 2.8 million jobs last month but that was much milder than the 9.3 million that economists told investors to expect.
One Australian dollar was buying 68.98 US cents at 1200 AEST, down from 69.37 US cents at the close on Wednesday.
Demand for iron ore is keeping the dollar hovering around its highest point since January.