Australia's Victoria state reported a record daily increase in COVID-19 cases while New South Wales said it was tightening some restrictions as authorities struggle to contain a new outbreak.
Helping investor sentiment, the Australian government on Thursday said it would inject a further A$1.5 billion ($1.05 billion) into a wage subsidy programme as the national unemployment rate hit a 22-year peak in June.
"It's (the market) sitting on a wall of worry right now," said Brad Smoling, managing director at Smoling Stockbroking.
"We have had such a sugar hit from all of the stimulus, we are taking a seat and wondering if we can keep going or start to fall over?"
The European Union will meet later in the day to discuss a proposed stimulus to kick-start the COVID-hit economy.
Mining stocks climbed 0.8%, led by a 4.4% rise in Alumina Ltd. South32 Ltd advanced 4.2%, while Rio Tinto closed 0.6% higher after touching a near six-month high earlier in the day.