In July 2012, verbal intervention by the European Central Bank president—his now-famous pledge to do "whatever it takes"—proved enough to halt the euro-zone debt crisis in its tracks. But it also set off a steady rally in the euro, which has risen around 15% against the dollar and 11% on a trade-weighted basis since then.

The euro's rise is now causing a headache for the ECB, because it risks pushing down inflation even further from its current low level of 0.8%. So Mr. Draghi, along with other ECB policy makers, is weighing in again: He said Thursday the euro had had a "significant" impact on inflation and was becoming "increasingly relevant" in assessing the outlook—a clear shot across the market's bows.

Mr. Draghi's comments had an immediate impact, pushing the euro around half a cent lower against the dollar, taking it off its recent highs approaching $1.40. But the euro rose again Friday morning. It is supported by a range of factors: perceptions of the ECB's stance, the euro zone's current-account surplus, ongoing flows into European assets, and the fact that the decline in inflation has pushed euro-zone real interest rates higher relative to those elsewhere, particularly in the U.S. While verbal intervention may have a short-term impact, it seems unlikely to produce a clear shift lower in the euro that might ease some of the strains facing the currency bloc.

In 2012, Mr. Draghi was able to follow up his words with the introduction of a mechanism for preventing speculative attacks on euro-zone government bonds. Now, the problem Mr. Draghi faces is that the policy decisions that would clearly unlock a durably lower euro—a negative deposit rate on cash held at the ECB, or quantitative easing—are highly controversial and may carry negative side-effects.

In the absence of ECB policy actions, the decisive force in pushing the euro lower likely lies in the hands of other central banks, in particular the U.S. Federal Reserve. Better U.S. data and a sense that the Fed wouldn't only continue cutting back its bond purchases but might start to shift toward discussing rate increases would turn the tide and boost the dollar. If U.S. short-term real rates rise by 0.25 point, Credit Suisse estimates that would unwind around a quarter of the support given to the euro against the dollar by rate differentials.

If the U.S. recovery picks up, Mr. Draghi's words might be enough: the euro should decline. But if it continues to climb—with $1.43-$1.45 viewed as the danger zone—Mr. Draghi may yet have to back words with deeds.