Global stocks and the euro soared after Europe and the International Monetary Fund announced 750-billion-euro (one-trillion-dollar) package of loans, guarantees and credits to ease the immediate crisis.
Central banks from the United States to Japan also played a crucial part in efforts to stop the Greek debt crisis spreading, as they agreed to intervene to ensure there was plenty of liquidity on the money markets.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
However, in Asia gains were limited and the euro eased back against other major currencies as investors focused on how the massive bailout will be carried out and the implications for the eurozone's underlying fiscal woes.
After rising to almost $1.31 overnight, the euro drifted back to $1.2804 in late New York trading, dropping as low as $1.2764. Late Friday, the euro was worth $1.2731.
Tokyo trimmed early gains to close up 0.08 percent at noon, while Sydney was 0.31 percent higher and Seoul lifted 0.45 percent.
Shanghai was 0.91 percent stronger as dealers digested data showing China's consumer prices rose 2.8 percent in April compared with the same month a year earlier, while industrial output expanded 17.8 percent in the same period.
However, they will keep an eye on the fact that house prices continued to soar and bank lending jumped last month.
Singapore added 0.32 percent.
However, Hong Kong edged 0.24 percent lower in early trade on profit taking after soaring 2.54 percent Monday.
The euro was also hit by a warning from Moody's Investors Service that it may downgrade Portugal and lower debt-laden Greece's rating to junk status, after a similar move by Standard & Poor's which saw borrowing costs spike for Athens.
"The EU's rescue package seems to have soothed immediate fears of a spreading of the European debt crisis," said Mike Jones, currency strategist at the Bank of New Zealand.
"However, market sentiment is still fragile and the eurozone's structural issues, including whopping budget deficits, still need to be addressed."
The debt crisis began as Greece teetered toward default, triggering fears that other weak economies such as Portugal, Spain and Italy may be next.
"The question is if (debt-ridden European) governments can exert leadership in pushing with austere measures," said Hideaki Inoue, a senior dealer at Mitsubishi UFJ-Trust and Banking Corp.
The euro members have given reassurances they would commit to austerity measures that will bring their fiscal positions back into line but markets remained cautious.
The British pound held at 1.4836 dollars after Prime Minister Gordon Brown said he would resign as Labour leader by September and hold talks with the Liberal Democrats on forming a government after a general election ended in stalemate.
Oil was higher. New York's main contract, light sweet crude for June delivery, gained 51 cents to 77.31 dollars a barrel while Brent North Sea crude for June soared 42 cents to 80.54 dollars.
Gold opened at 1,202.00-1,203.00 US dollars an ounce in Hong Kong, up from Monday's close of 1,187.50-1,188.50 dollars.
