The euro hit its lowest since early 2006 on Monday, unsettled by the expectations of monetary easing and concerns about Greece that kept the currency under pressure at the back end of 2014, Reuters reported.
The dollar rose across the board, starting 2015 as many investors believe it intends to go on.
The euro dived below $1.20, falling as low as $1.18605 in Asian trade. It recovered some ground but by 1109 GMT was again looking shaky at $1.1905, down 0.8 percent on the day. Against the yen, it hit a two-month low of 143.15 yen, down 1 percent on the day.
Sterling was down 0.5 percent at $1.5245, having fallen to a 17-month low of $1.5185 in Asian trading. The yen fared better, gaining 0.2 percent on the day at 120.26 yen per dollar.
Dealers in London said there was room for a pause in dollar strength, with some seeing strong support for the single currency around $1.1850.