The franc has shadowed the euro against other currencies since the Swiss National Bank imposed a 1.20 per euro cap more than a year ago after safe haven inflows had pushed the franc to record highs and threatened to tip the Swiss economy into recession.
The single currency, and by extension the franc, came under pressure as concerns surfaced about how Greece will implement reforms to meet a new debt target which will enable it to secure more financial aid and avoid a chaotic default.
"The realisation that any aid to Greece will still be subject to several parliamentary approvals, ongoing reforms and a successful debt buy back may have dampened sentiment or more likely the deal was already priced in," said Credit Agricole foreign exchange strategist Mitul Kotecha in a note.
Worries about the looming US "fiscal cliff" of tax increases and spending cuts which could kick in early next year also weighed on risk appetite, buoying the dollar and pressuring the euro.
The franc traded 0.2 percent lower against the dollar compared to the New York close, changing hands at 0.9315 francs per dollar by 0703 GMT.
The franc was little moved against the euro at 1.2037 francs per euro.