The euro rose for a second day against the dollar on Tuesday before a meeting of the U.S. Federal Reserve that may push back expectations for when U.S. interest rates will start to rise.
The Swiss franc fell after the Swiss National Bank said it was ready to intervene in the market to curb gains by the currency since it lifted its cap on the franc's value. The franc lost 2 percent against the euro to trade as low as 1.03845.
The euro rose as much as 0.9 percent to trade at $1.13455, lifting it further from an 11-year trough of $1.1098 reached on Monday, when it became clear that Greece had voted in a new anti-bailout government.
Investors are hopeful that the left-wing Syriza party leader, Alexis Tsipras, is willing to negotiate, easing concern that a confrontation with its international creditors could lead Greece to leave the euro.