The franc was down 0.2 percent against the euro compared to the New York close, trading at 1.2971 per euro at 0636 GMT.
The franc was down 0.3 percent against the dollar at 0.9225 per dollar, well off the historic peak it hit around 0.8963 on March 17, due to turmoil in the Middle East.
"Undervaluation of the dollar versus the franc will most likely be the stabilizing factor because yield spreads are likely to remain at very narrow levels," said Credit Suisse analyst Marcus Hettinger in a note.
The euro slipped against the dollar after German Chancellor Angela Merkel's conservatives were routed in elections in a key state, but was supported against the franc by prospects of a European Central Bank rate rise.
The dollar was also helped by Friday's comments from a US central bank official who said the Federal Reserve is poised in the "not-too-distant future" to begin rolling back its super loose monetary policy to avert inflation.
But further Western air strikes in Libya and tension in Syria, Yemen and Bahrain are likely to support the safe-haven franc with SEB technical analyst predicting further euro weakness.
"Initial support likely half way down Friday's range around 1.2920," they said in a note.
"Also below the March 23 low of 1.2737 is needed to deem the ongoing lift as correctional and get back the panic low of 1.2401 on the edge of the radar again."
The franc hit an all-time record of 1.2400 against the euro in late December on fears about debts in some euro zone countries but analysts say the euro is unlikely to enter another downtrend, given expectations for an ECB hike next week.
The Swiss National Bank has its target for the 3-month Swiss franc LIBOR ultra low, and many economists expect the SNB to wait to hike rates -- despite robust domestic conditions -- until after the ECB.