In prepared testimony to the Senate Banking Committee, Greenspan said the US economy was expanding at a healthy pace and that despite rate hikes by the Fed, the real fed funds rate "remains fairly low". He will give the second part of this twice-yearly testimony later on Thursday.
Earlier this month, Greenspan had caused ripples through financial markets after a speech in London where he sounded upbeat on prospects for a narrower US current account deficit, a key driver of the dollar's decline in recent years.
The euro stood at 1.5475 francs, from levels of 1.5475/80 on Wednesday.