The euro bought $1.2786 in Tokyo, against $1.2791 late Monday in New York where the single currency had briefly fallen to $1.2767, its lowest level since September 11.
The dollar and euro both weakened versus the safe-haven Japanese currency, with the euro buying 102.37 yen, compared with 102.69 yen in New York, while the dollar fetched 80.06 yen from 80.28 yen.
Markets were keeping a close eye on the neck-and-neck race between President Barack Obama and Republican challenger Mitt Romney for the White House, with results due out on Wednesday morning in Asia.
Hiromichi Shirakawa, an analyst at Credit Suisse in Tokyo, said an Obama win has been viewed as a dollar-selling cue, with the fading likelihood of further Bank of Japan easing measures in November lifting the yen.
“The yen could shoot up from late November,” he added.
The euro was hit by worries over Greece and a possible rate cut by the European Central Bank (ECB) aimed at injecting new life into the continent’s economy.
“At the moment Greek risks are spawning euro selling,” Shirakawa said.
“If the Greek parliament votes down a reform package and the ECB goes ahead with a rate cut… we cannot rule out the possibility that the euro would plunge to around $1.25,” he said in a note.
Greece has been negotiating with its international creditors to unlock the latest tranche of a bailout package necessary to avoid a default.
The dollar was also mixed against other Asia-Pacific currencies.
It fell to Sg$1.2240 from Sg$1.2241 Monday, to Tw$29.22 from Tw$29.24, to 1,091.20 South Korean won from 1,091.65 won and to 41.23 Philippine pesos from 41.27 pesos.
It rose to 30.81 Thai baht from 30.79 baht and to 54.65 Indian rupees from 54.13 pesos while it was unchanged at 9,633 Indonesian rupiah.
The Australian dollar rose to $1.0432 from $1.0359 while China’s yuan edged down to 12.81 yen from 12.85 yen.
— Dow Jones Newswires contributed to this report —