The single currency fell as much as 0.3 percent against the dollar to $1.1339 and declined by a similar margin against the Swiss franc to 1.1269 francs.
Its biggest decline was against the British pound , falling half a percent at 89.53 pence, with relief that British Prime Minister survived a no-confidence vote also boosting the British currency.
German 10-year government bond yields dropped more than a basis point as Draghi spoke to trade flat on the day at 0.27 percent.
Other high-grade euro zone bond yields also fell 1-2 basis points.
Euro-zone stocks trimmed their gains slightly and were last up 0.1 percent after the drop in the euro boosted shares.