The dollar is near a record low around $1.31 per euro today but remains steady against the yen after Russia suggested it might buy more euros, while Asian stocks rose on expectations of good earnings.
News that Russia may consider boosting the share of euros in its $100 billion-plus currency reserves and a rebound in oil prices that is clouding the US economic outlook helped to undermine the dollar.
Japan's Nikkei average closed up 0.21 percent at 10,872.33, as bargain hunting in domestic-related issues outweighed selling of exporters such as Canon Inc.
By 0610 GMT, an MSCI index of non-Japanese Asian shares had risen 0.67 percent, its highest levels in almost 5 years.
Japan Tobacco Inc. jumped 2.13 percent, while Mitsui O.S.K. Lines, Japan's number two ocean freight firm, climbed 4.58 percent.
"We're seeing a slight rebound but the market is still wondering if the yen is going to strengthen above 100," said Junichi Misawa, fund manager at STB Asset Management.
"We are also facing more holidays for the U.S. market so there's nothing there to drive the market higher," he added, referring to Thursday's Thanksgiving holiday.
Australian stocks touched a record high, supported by gains in BHP Billiton. The benchmark S&P/ASX 200 index hit an all-time high of 3,889.8, before easing slightly to close up 0.42 percent at 3,882.5.
BHP Billiton put on 1.08 percent, extending Tuesday's gains after it completed a bigger-than-expected A$2.3 billion ($1.8 billion) buyback of 4.8 percent of its Australian-listed shares.
Most other Asian share markets were higher, led by a 1.41 percent gain on South Korea's KOSPI. Hong Kong was up marginally heading into the afternoon, looking to set a fresh 3-1/2-year closing high.