With most speculators already running big bets against the euro, traders said, only a weaker-than-expected inflation reading of 0.4 percent or lower would have taken the euro below $1.36 - levels last seen in mid-February.
The euro was trading 0.1 percent higher above $1.36, having fallen immediately after the inflation data was released, taking it close to a 3-1/2 month trough plumbed late last month.
The ECB is widely expected to loosen policy when it meets on Thursday. Measures are expected to include negative deposit rates, the rates at which banks park excess cash with the ECB, and that could see the euro come under more pressure, analysts said.
Traders said for the euro to drop sharply, the dollar has to strengthen further. U.S. factory orders for April are due on Tuesday and a robust number may boost Treasury yields and help the dollar.
The dollar hovered near a four-month high against a basket of major currencies bolstered by recent upbeat U.S. data.
Trading was choppy in Asia, reflecting some confusion after the U.S. Institute for Supply Management corrected its manufacturing activity index for May to 55.4, from a below-consensus reading of 53.2. The ISM said it had to make the correction due to an error in applying the seasonal adjustments.
U.S. Treasury yields rose as a result, helping boost the dollar's allure. The dollar index stood just below 80.60, within close reach of Monday's four-month high.
Against the yen, the U.S. currency was flat at 102.40, having risen 0.6 percent on Monday in its biggest one-day rise in over two months.
The Australian dollar inched up after the Reserve Bank of Australia kept interest rates unchanged and refrained from trying to talk the currency down as some market watchers had speculated. It rose 0.3 percent near $0.93.
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