The euro eased back on Tuesday but was still on track to be the world's best-performing major currency this year, while the dollar was set for its biggest annual gain against the yen since 1979.
The euro has gained 26 percent against the yen this year, though it fell 0.1 percent to 145.03 yen on Tuesday, having set a five-year high of 145.67 yen on Friday.
Against the dollar the euro has gained more than 4 percent, baffling many hedge funds who had expected a weak euro zone economy and a reduction in Federal Reserve bond-buying to strengthen the greenback this year.
The Fed, however, finally announced its first move earlier this month and a steady reduction in the flood of dollars it is pumping into the economy looks set to contrast starkly with the Bank of Japan next year.
(Read more: Resurgent carry trade to keep yen weak)
"We think things are going to be very data-dependent,'' said Paul Chappell, CIO of UK-based hedge fund manager C-View.
"At the moment that looks like U.S. numbers are going to be relatively robust compared with some other G7 peers, so the dollar is likely to be relatively robust versus other developed country currencies.''
He said the euro, boosted recently by banks in the region repatriating funds to shore up their capital bases, tends to lose ground in the first few days of a new year.
On Tuesday the euro was 0.2 percent down to $1.3782 as the gap between U.S. two-year government bond yields and German yields widened, increasing the relative attractiveness of the dollar.
(Read more: Yen set for worst year since YMCA topped the charts)
Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation in Singapore, saw the dollar rising to 110 yen in the first half of 2013, before retreating below 100 yen mid-year and then re-testing 110 yen in late 2014.
The Swiss franc hovered near a three-decade peak against the yen, fetching 118.22 yen. The franc touched 119.17 yen on Friday, its highest since January 1983.