The cap of 1.20 per euro set by the Swiss National Bank a year ago to ward off deflation and a recession means the franc usually trades in tandem with the euro against the dollar.
Jittery investors kept the franc trading just shy of the 1.20 mark for months.
Yet an easing of tensions in the euro zone following the European Central Bank's bond buying announcement last month has allowed the safe-haven unit to slip against the common currency. Uncertainty about when Spain might seek foreign financial aid has kept a lid on the euro's gains.
The franc fell 0.1 percent against the dollar to trade at 0.9283 at 0706 GMT. Against the euro, the franc was flat at 1.2107, compared to the New York close.
With the Swiss economic calendar sparse this week, trading in the franc was expected to be lackluster.
"We do not expect much in terms of investor appetite and activity," said Informa Global Markets analyst Tony Nyman.
A softening of economic fundamentals in Switzerland, including a slight contraction of the economy in the second quarter, has reinforced the SNB's justification for the cap.
Swiss Economy Minister Johann Schneider-Ammann said during a speech late on Monday the cap was "absolutely essential" to safeguard the economy.
Although the SNB had to intervene by selling hundreds of billions of Swiss francs earlier this year to defend the cap, the franc's slipping to around 1.21 per euro has granted the central bank some breathing space.
The amount of cash commercial banks hold with the SNB, called sight deposits and considered an gauge of the SNB's interventions, fell slightly last week, data on Monday showed.
"The latest data clearly hint at an SNB that is less involved on financial markets compared to prior months," UBS economist Reto Huenerwadel said.