The euro rose to $1.2985 from $1.2939, while the dollar was trading at 76.85 yen from 76.98 late Friday in New York. Markets were closed Monday and Tuesday in Japan for public holidays.
The European unit also firmed against the yen, changing hands at 99.79 against 99.62 late Friday.
"With the euro facing capitulation risks in (the first quarter), the first half of the year is likely to favour the US dollar as a safe haven currency," Singapore's DBS bank said in a commentary.
"The eurozone sovereign debt crisis is no longer only about the peripheral countries.
"Rating agencies have placed the whole region on negative watch including the AAA-rated core EU economies."
DBS bank said it expects the euro to decline to $1.20 by the end of this quarter.
The eurozone's still-unresolved fiscal woes have dented the single currency with Spain announcing Friday 8.9 billion euros in budget cuts and higher taxes as it moves to curb a bigger-than-expected public deficit.