A drop in German business sentiment to its lowest since early 2010 stoked concerns about a slowdown in the euro zone's largest economy.
Spain also remained in focus, on concerns that the country is dragging its feet in requesting the international bailout that most market participants expect.
The franc has spent much of the last year trading in lockstep with the euro against the dollar after the Swiss National Bank set a cap of 1.20 per euro on Sept. 6, 2011 to stave off a recession and deflation.
Yet as signs have mounted that the euro zone crisis may be easing following the European Central Bank's plan to buy the bonds of troubled member states, the franc has been losing ground against the euro.
Mitul Kotecha, head of global forex strategy at Credit Agricole's investment bank, said risk aversion was gaining ground among market participants once again, given the concerns about a possible Spanish bailout and Greece's budget woes.
"The near term outlook is likely to remain one of caution until some progress in the eurozone is in evidence," Kotecha said.
"However, growth concerns suggest any improvement in sentiment will be tenuous at best."
SNB Chairman Thomas Jordan will speak at a business event in Pfaeffikon, Schwyz at around 0800 GMT.
"We expect Jordan to stick by and large to the rhetoric included in their official statement once more," UBS economist Reto Huenerwadel said. "Any softening of the SNB's position on monetary policy is unlikely to materialise anytime soon."
The franc was down 0.2 percent against the dollar to trade at 0.9371 by 0549 GMT compared to the New York close, having fallen as far as 0.9391 on Monday, its weakest since Sept. 13.