The euro was supported by minutes of the US Federal Reserve's last policy meeting, which raised expectations the Fed may start a fresh round of stimulus next month.
But many in the market are awaiting Friday's speech by US Federal Reserve Chairman Ben Bernanke at an annual informal meeting of central bankers at the US retreat of Jackson Hole.
SNB Chairman Thomas Jordan will not attend the meeting in Jackson Hole this year, due to a scheduling conflict with a meeting of the SNB's supervisory board, a spokesman said.
For the past year, the franc has been trading in tandem with the euro against the dollar after the Swiss National Bank set a cap of 1.20 per euro on the safe-haven franc on Sept. 6 to reduce the risk of a recession.
In an interview to mark the cap's one-year anniversary, SNB Chairman Thomas Jordan said it remained the right policy tool for now. The SNB holds its next policy review on Sept. 13 and is expected to stick to its policy of low interest rates and the cap on the franc.
The SNB's spiralling forex reserves - which hit nearly 70 percent of annual output in July - have raised questions as to how long the central bank can sustain its policy of currency interventions to halt the franc's rise at 1.20.
"The SNB shows no signs whatsoever of stepping away from the lower boundary in euro/Swiss at 1.20 anytime soon," said UBS economist Reto Huenerwadel.
Real estate prices and mortgage lending have risen strongly in Switzerland, a by-product of the SNB's ultra-low interest rates. In July authorities enacted new regulation to lessen the chance of overheating.
On Monday the SNB said it would forego enacting a capital buffer for banks' mortgage risks for now, saying the property market showed signs of cooling.
"A well behaved housing market according to the SNB and the by no means increased inflationary pressures make a case for an unchanged SNB policy for at least another quarter," Huenerwadel said.
The franc fell 0.1 percent against the dollar to trade at 0.9617 by 0516 GMT compared to the New York close.
The franc was flat against the euro at 1.2010.