But analysts said there was still plenty of scope for disappointment if policymakers did not resolve liquidity and solvency issues in Europe.
"It's a knee-jerk reaction to the world failing to come to an end last night," said E.L. & C. Baillieu Stockbroking director Richard Morrow.
"It is a reversal and I don't see it lasting. The market has been as gloomy as I can remember since the last days of 2008," he said.
Among the large-cap stocks rebounding from recent steep losses were Macquarie Bank , up 5.6 percent, and global miner Rio Tinto , up 3.5 percent.
Euro zone officials are working to magnify the firepower of the region's rescue fund and begun discussing the next steps to shore up the financial system and prevent the crisis from derailing a fragile world economic recovery
"There are much more positive signs coming out of Europe, and once we can quantify the actual exposures (of the banks), the markets will draw more comfort. It is the uncertainty that has really affected the markets," said CMC Markets analyst Michael McCarthy.
The benchmark S&P/ASX 200 index jumped 97 points to 3,960.9 at 0118 GMT, the biggest gain in three weeks, but still shy of the psychological 4,000 level. The benchmark lost 1 percent on Monday.
New Zealand's benchmark NZX 50 index rose 1.1 percent to 3,291.7.
STOCKS ON THE MOVE
Midcap resources stocks surged after recent selling, with coal miner Aquila Resources gaining 6 percent, base metals miner Kagara up 7.7 percent and rare earths miner Lynas Corp jumping 16 percent, and were the most actively traded stock.
Lynas shares were "absolutely slaughtered" in a brutal sell-off on Monday falling 21 percent, and were merely recovering, according to Argonaut senior dealer James McGlew. He said heavy volumes indicated hedge funds were playing volatility in the resources sector.
Linc Energy shares surged 8.1 percent to A$1.81 after announcing a significant oil shale deposit in South Australia.
Food manufacturer Goodman Fielder shares remained in a trading halt after it announced plans to raise A$259 million through a share issue to bolster is balance sheet.