The euro fetched $1.4379 in Tokyo morning trading, down from 1.4431 in New York late Friday. The single European currency was at 119.33 yen, down from 119.91.
The dollar was lower at 82.98 yen, compared to 83.09.
The euro came under pressure on Friday after Moody's cut its credit rating on Ireland by two notches to just above junk status, citing an "expected decline" in government finances that is set to hamper the nation's recovery.
Sentiment worsened after the Wall Street Journal reported over the weekend that the International Monetary Fund believes Greece's debt is unsustainable.
The IMF has told European government and central bank officials that Athens should consider restructuring by next year, according to the report.
"The market is focusing on euro selling, as the news about restructuring debt in Greece rekindled worries," said Gen Kawabe, dealer at Chuo Mitsui Trust and Banking.
Daisaku Ueno, chief analyst at Gaitame.Com Research Institute, told Dow Jones Newswires: "Recent sharp gains in the euro so far this year may have priced in multiple rate hikes by the ECB, and resurfacing European sovereign debt issues may have offered investors a good cue to take profits."
The European Central Bank hiked interest rates earlier this month for the first time in nearly three years although it signalled at the time that this did not necessarily mean that more were to follow immediately.
Finland's weekend election also added to the pressure, said dealers.
The True Finns party which is against bailouts for deeply indebted eurozone countries won 19 percent of the vote, improving the chance it will be part of Finland's new coalition government.
Any opposition from the new Finnish government to further bailouts for eurozone countries could theoretically prevent the European Union from granting new rescue loans, since they have to be agreed unanimously by all members of the single currency.
Ueno said the weak Japanese stock market also put pressure on the euro versus the dollar.
Meanwhile, the dollar was weighed down against the yen on receding expectations for the Federal Reserve's early exit from its quantitative easing monetary policy, dealers said.
Expectations for a rate hike waned after US government data released Friday showed that core inflation data posted a smaller-than-expected rise of 0.1 percent in March.