The single currency bought $1.2785 and 101.53 yen in Tokyo afternoon trade, lower than $1.2815 and 101.62 yen in New York late Monday. The dollar was changing hands at 79.38 yen against 79.30 yen.
There was little new to move the euro although the currency may win a measure of support from hopes European leaders will agree on measures to calm nervous markets at their meeting in Brussels on Wednesday, dealers said.
"The fall is not news-driven," a dealer at a Japanese bank told Dow Jones Newswires.
The euro was little changed after French Finance Minister Pierre Moscovici said Tuesday that a Greek exit from the eurozone risks causing an "unpredictable" spread of Europe's debt crisis.
However, the unit may edge higher as traders close out short positions, said Osao Iizuka, head of FX trading at Sumitomo Mitsui Trust Bank.
"Sentiment has improved somewhat after the weekend G8 summit, even though the dire situation in Greece remains unchanged," he said.
In a note, National Australia Bank said: "We expect markets will attempt to broadly hold on to the rebound ahead of Wednesday's EU leader meeting. That said, investors remain biased to sell the growth/risk currencies."
On Monday, leaders of the Group of Eight major economies backed debt-stricken Greece to stay in the eurozone, boosting the euro amid fears Athens would exit the beleaguered bloc as sentiment against austerity cuts deepen ahead of fresh elections next month.
The dollar was mostly lower against most other Asian currencies.
It slipped to Tw$29.52 from Tw$29.55 on Monday, to Sg$1.2671 from Sg$1.2707, to 1,163.80 South Korean won from 1,167.55 won and to 9,300.00 Indonesian rupiah from 9,350.00 rupiah.
But the dollar strengthened to 31.30 Thai baht from 31.21 baht while holding steady at 43.16 Philippine pesos.