In Europe, the Stoxx 600 Index ended the day with a 2.1 per cent gain, recovering from losses earlier in the session.
In afternoon trading in New York, the Dow Jones Industrial Average advanced 1.36 per cent, the Standard & Poor's 500 Index climbed 1.31 per cent and the Nasdaq Composite Index rose 1.51 per cent.
"Right now the market just reacts to whatever rumour and whim is out there, going back and forth. What is Greece going to do? What is Germany going to do? What is Merkel saying, what is the meeting doing?" Cliff Draughn, chief investment officer at Excelsia Investment Advisors, told Reuters.
"Sooner or later Europe will solve the problem. There is going to be some pain in between, but they will solve the problem," Draughn said.
Gains on equity markets lowered the appeal of US Treasuries. Yields on 10-year notes climbed seven basis points to 2.06 per cent while those on 30-year bonds rose eight basis points to 3.10 per cent in early afternoon trading in New York, according to Bloomberg.
"We're seeing pressure on the long end because of positive developments out of Greece and the ECB cut provided a boost of the equity markets," Dan Mulholland, a Treasury trader in New York at RBC Capital Markets, told Bloomberg News.
"With the market already trading at lower yields than it should be based on fear that the European situation could escalate even worse, we're seeing pressure on the long end. We also have supply next week," Mulholland said.
For now, the euro benefitted from the cautious optimism, strengthening 0.8 per cent to US$1.3850 in New York afternoon trading. It had dropped as much as 0.7 per cent earlier in the day.
Even so, gains will likely be limited as there are plenty of economic and fiscal hurdles ahead, analysts said.
The ECB's Draghi today also signalled expectations that the region's economy will get worse before it gets better.
"What we are observing now is ... slow growth heading toward a mild recession by year-end," Draghi told a news conference, according to Reuters. "A significant downward revision to forecasts and projections for average real GDP growth in 2012 [is] very likely."