The franc has shadowed the euro against the dollar since last September, when the Swiss National Bank set a cap of 1.20 on the safe-haven unit to stave off recession and deflation.

"The dollar-Swiss franc is just a function of euro dollar at the moment. With no imminent deflationary risk, the SNB can maintain their current policy, with no risk to keeping the lower barrier," said Commerzbank currency strategist Antje Praefcke.

"There is little to say about the euro-Swiss franc at the moment, and volumes remain pretty low, even though there is still the tendency to buy the Swiss franc on spikes in risk aversion."

Despite the slight decline in the current session, the franc remains close to a month high against the euro.

Credit Agricole analysts said that beyond Draghi's defence of the euro, there were technical indications that euro bears should take a back seat while the euro uptrend remains intact.

"Three-day price action in EUR/USD suggests that a pattern of higher-lows may be setting in, and a failure to break and close below 1.2370/80 for the remainder of the week could open the door to a re-test of late June levels between 1.2550 and 1.2610 by the middle of August before new structural selling opportunities present themselves," they said.

The franc fell 0.1 percent against the dollar compared to the New York close, trading at 0.9698 francs per dollar at 0632GMT.

The franc was little changed against the euro at 1.2010 francs per euro.