The franc has shadowed the euro since Swiss National Bank imposed a lid on the safe-haven currency at 1.20 per euro in September 2011 to try to prevent deflation and a recession.
The SNB is expected to reiterate its commitment to keeping a lid on the franc when it announces its quarterly monetary policy decision at 0830 GMT on Thursday.
A Reuters poll published last week showed the SNB will maintain the cap it set on the franc at least through 2013 and possibly even into 2014, while also keeping interest rates near zero.
The franc fell 0.2 percent against the dollar to trade at 0.9359 by 0718 GMT compared to the New York close. The franc rose 0.1 percent against the euro to trade at 1.2074.
"USD/CHF has seen a strong rebound from the 0.9240 support area - this support zone has been repeatedly tested over the past two weeks and we suspect that the market has based for now," said Commerzbank analyst Karen Jones.
Data published on Friday showed the SNB's foreign exchange reserves fell for a second month running in November, showing little need for the central bank to intervene to defend the 1.20 limit.
"Our expected trend for a slowdown and then reversal in safe haven franc inflows appears to have been confirmed," said Credit Agricole analyst Adam Myers.
"The question in our opinion is now whether the SNB will be forced to buy francs thereby 'controlling' any abrupt franc decline. We look for EUR/CHF to grind higher under such conditions, breaking last week's 1.2170 resistance area."