At 10:30 (AEST), the benchmark S&P/ASX 200 index was up 148.70 points or 2.87 percent at 5,330.10, while the broader All Ordinaries index was up 154.10 points or 2.97 percent at 5,348.10.
The moves come after the government announced a 130 billion Australian dollar (79.8 billion U.S. dollar) subsidy package for workers.
The announcement of the package saw Australia's share market surge in the last hour of trading on Monday to finish around 7 percent higher, the market's best single day result ever.
"After massive underperformance Friday, the ASX 200 rebounded very sharply, with its 7 percent gain the largest on record," Westpac economists said in a morning note.
"Late in the day, the federal government announced its well-flagged 'jobkeeper' payments to employers, the largest fiscal measure yet."
On Tuesday most sectors were firmly improved, excluding materials and consumer staples which eased.
In the financial space, Australia's big banks rallied with the Commonwealth Bank up (4.93 percent), ANZ up (5.90 percent), National Australia Bank up (5.89 percent) and Westpac Bank up (5.97 percent).
Mining stocks were mixed with Rio Tinto up (0.66 percent), BHP down (1.09 percent), goldminer Newcrest down (4.37 percent) and Fortescue Metals down (0.40 percent).
The country's oil and gas producers bounced with Oil Search up (5.58 percent), Santos up (4.14 percent) and Woodside Petroleum up (2.39 percent).
Australia's largest supermarkets sank with Coles down (6.18 percent) and Woolworths down (2.33 percent).
Meanwhile, telecommunications giant Telstra sank (0.62 percent), the national carrier Qantas lifted (3.59 percent) and biomedical firm CSL lifted (2 percent).
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