Poor performances by pro-bailout parties in Greece and the victory of Francois Hollande in France, who wants to focus more on growth, have cast doubt on European austerity plans.
The euro fell as low as $1.295, its lowest since January, and dropped to three-year lows against the pound.
The main European stock markets fell early on before recovering.
In Germany, the Dax fell by more than 2%, but by mid-afternoon was only down by 0.5%.
In Paris, the Cac 40 recovered to trade up by 0.3%.
Athens shares fell by as much as 8.3%. In London, markets were closed for a bank holiday.
The interest rates on some government debt has also gone up, indicating a fall in investor confidence. The yield in the secondary markets for Greek 10-year bonds has gone up from 20% to 22.2%.