Weakness in the dollar, which was hurt following data that showed US consumer confidence fell sharply in May and a weak reading for business confidence in the US Midwest, helped support prices for oil and other commodities. Crude rose more than 1.5 percent, while copper hit a four-week high.
In equity markets, energy and other commodity shares rose on Wall Street, while in Europe banking stocks led gains, with Greek banks up 10.1 percent.
European officials met in Vienna to sketch out options for a second bailout package for Greece, with private sector participation still under discussion to help relieve the country of its heavy debt burden.
Germany is considering dropping its push for an early rescheduling of Greek bonds in order to facilitate a new package of aid loans for Greece, The Wall Street Journal reported, citing people familiar with the matter.
"More aid for Greece does not solve the problem, but it does buy time and limit contagion risk into Ireland, another country with funding requirements in 2012," said Camilla Sutton, chief currency strategist at Scotia Capital in Toronto. The euro rose as high as $1.4424 to the dollar, according to electronic trading platform EBS.
But even as the euro strengthened on Tuesday, there were doubts that gains could be sustained.
"I would fade this rally in the euro for now," said Valentin Marinov, currency strategist at Citi. "Investors will be looking for a more lasting resolution to the Greek debt problems and our economists haven't ruled out the possibility of a voluntary restructuring involving private bondholders."
On Wall Street, the optimism on aid for Greece drove sentiment, overshadowing another round of weaker-than-expected US economic data.
The Conference Board, an industry group, said its index of consumer attitudes fell to 60.8 from a revised 66.0 in April. The reading was below economists' forecasts for 66.5.
The Institute for Supply Management-Chicago's index of Midwest business activity fell in May to 56.6 from 67.6 in April.
Separately, US single-family home prices dropped in March, dipping below their 2009 low, as the housing market remained bogged down by inventory and weak demand, the S&P/Case Shiller composite index of 20 metropolitan areas showed.
The Dow Jones industrial average was up 62.40 points, or 0.50 percent, at 12,503.98. The Standard & Poor's 500 Index was up 6.61 points, or 0.50 percent, at 1,337.71. The Nasdaq Composite Index was up 15.96 points, or 0.57 percent, at 2,812.82.
The pan-European FTSEurofirst 300 index of top shares closed 0.8 percent higher at 1,141.24 points, a 2-1/2 week closing high.
MSCI's all-country world stock index rose just over 1 percent, while its emerging market index gained 1.7 percent.
The euro pared some of its early gains after a German member of parliament told business newspaper Handelsblatt that Greece should leave the euro zone.
May marked the euro's worst month since November, with the single currency weighed down by fears that a new aid package would provide only temporary relief to Greece rather than the intensive surgery required for the country's financial ailments.
The dollar was down about half a percent against a basket of currencies.
Other assets seen as risky also gained. Copper rose to a four-week high, supported by a firmer euro, and the Reuters/Jefferies CRB Index of 19 commodities was up 1.2 percent.
US crude oil rose 1.60 percent to $102.19 per barrel, while Brent crude rose 1.67 percent $116.60.
Assets seen as havens in times of uncertainty or perceived turmoil fell. The benchmark 10-year US Treasury note was down 1/32 in price to yield 3.06 percent. Spot gold prices fell $1.26 to $1,536.60 an ounce.
Copyright Reuters, 2011