A statement by Greek prime minister Lucas Papademos said Greek political leaders have agreed on all points of a bailout package except one, on which talks will continue with the country's international lenders.
Greek party officials said the level of cuts in pensions remained the sticking point but discussions with the "troika" of international lenders would continue so a deal could be concluded before a meeting of euro zone finance ministers on Thursday.
"Short-term players reacted to the headlines," said a trader at a U.S. bank.
The euro fell as low as $1.3215 from late New York's $1.3260 and off a two-month high of $1.32890 hit on Wednesday before recovering some ground to $1.3253.
It has gained nearly 5 percent from a 17-month low of $1.2624 hit in January as the market has bet Greece will hammer out its second bailout deal with international lenders.
Immediate resistance is seen around its 90-day average at $1.3321 and 100-day moving average at $1.3332.
Market players said any deal would likely offer only a short-term boost to the euro given ongoing uncertainties about Greece and other euro-zone economies.
"The market has been thinking that there will be a second bailout package after all. You can't blame just Greece for the euro zone's slowdown. The economy is slowing because of tight fiscal policy," said Makoto Noji, a senior strategist at SMBC Nikko Securities.
Italy's economy, the currency bloc's third-largest, likely contracted in the fourth quarter, while countries such as Spain and Belgium have already reported contraction in the same quarter.
Against this backdrop, the European Central Bank is expected to follow an easing bias.
The ECB is likely to keep interest rates on hold at its policy meeting on Thursday but it may signal it is ready to cut rates in March.
Market players also expect banks to borrow about 400 billion euros from the ECB at its second cheap three-year funding operation planned at the end of the month, which many think is tantamount to a form quantitative easing.
While the Federal Reserve has indicated it is ready to ease policy further, a string of positive U.S. economic data in recent months has curtailed expectations of more easing, at least for now.
The Australian dollar fell 0.5 percent to $1.0749, having fallen about a full cent from a six-month high of $1.0845 hit on Wednesday after Chinese consumer inflation exceeded market expectations, reducing hopes of immediate easing by Chinese authorities.
The U.S. dollar hardly budged against the yen at 77.15 yen , a near two-week high of 77.19 yen hit on Wednesday, though Tokyo traders see limited chances of the U.S. currency breaking above last month's high of 78.29 yen given offers from Japanese exporters lined up towards 78 yen.
The yen is in part undermined by a fall in Japan's current account surplus -- a major and constant support for the yen. Data showed on Wednesday the surplus fell 44 percent to a 15-year low last year, as exports fell after the March earthquake and tsunami hit factories and oil imports soared as most of the Japan's nuclear power plants closed.
The size of the current account surplus, at 9.6 trillion yen, is smaller than the total of country's yen-selling intervention of 14.3 trillion yen, meaning there is little reason for the yen to gain from corporate currency flows.