The euro has now broken below support at $1.3310, the 38.2 percent retracement of its November-February rally, and its 55-day moving average at $1.3285. The losses leave it open for a test of the Jan. 10 low of around $1.3040.
Against the yen, the euro fell to 122.23 yen, its weakest level since late January. It was last at 122.78, down 1.2 percent.
David Mackie, European economist at JPMorgan in London, said that although the euro zone is making progress, the past month has seen a broad-based disappointment on the macroeconomic front, which would be enough reason for the ECB to cut rates.
The dollar index, which measures the greenback versus a basket of currencies, rose to a session peak of 81.508, the highest since early September, before easing slightly to trade at 81.37, up 0.4 percent on the day.
Fed officials are increasingly worried about the costs and risks of their quantitative-easing program, the Fed minutes showed on Wednesday, fueling expectations the central bank may scale back its stimulus program sooner rather than later.
"There will be less dilution of the value of the U.S. dollar, especially relative to the yen and maybe sterling," said Tatjana Michel, director of currency analysis at Charles Schwab in San Francisco.
Both the Bank of Japan and Bank of England are considering printing more money and expanding their balance sheets, driving down the value of their currencies.
Some analysts, however, said the dollar's reaction to the Fed minutes was overdone as the Fed's views on exit strategies are still evolving. BNP Paribas recommended buying the euro against the dollar, with a target of $1.38.
The dollar also rose to a one-month high against the Swiss franc of 0.9333 franc, and a four-month peak against the Australian dollar.
Against the yen, the dollar fell 0.5 percent to 93.10. The yen has been the worst-performing major currency so far in 2013 as investors bet on more aggressive policies from the Bank of Japan to reflate the world's third-biggest economy.
Morgan Stanley strategists said the dollar's decline was likely to be limited around the 92.90 yen area, the low struck on Feb. 12, before rising again to test its recent near three-year highs of around 94.50 yen.