The dollar extended losses from last week after a sharp drop in US consumer confidence for May and a weak reading for business confidence in the US Midwest. That boosted prices of commodities, with crude oil rising more than 1.5 percent and copper hitting four-week highs in London.
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. 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.
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.
The Dow Jones Industrial Average was up 47.00 points, or 0.38 percent, at 12,488.58. The Standard & Poor's 500 Index was up 4.54 points, or 0.34 percent, at 1,335.64. The Nasdaq Composite Index was up 13.81 points, or 0.49 percent, at 2,810.67.
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.
The dollar was down nearly half a percent against a basket of currencies. Other assets seen as risky also gained.
Oil prices rose almost $3 per barrel, reaching a session high above $103 per barrel in New York and $117 in London.
Benchmark copper on the London Metal Exchange closed at $9,220 a ton from a close of $9,199 on Friday. It earlier hit $9,278.50, its highest since May 4.
The Reuters/Jefferies CRB Index of 19 commodities gained as much as 1.2 percent.
Assets seen as havens in times of uncertainty or perceived turmoil fell. The benchmark 10-year US Treasury note was down 4/32 in price to yield 3.05 percent.
Spot gold prices fell more than $1 to hover around $1,536 an ounce.
