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The euro bought 141.90 yen, approaching its October 2008 high of 142.00 yen. Against the dollar, the euro bought $1.3736, moving toward its two-year high of $1.3833 set in October.
The dollar rose slightly to 103.31 yen, not far from its five-year peak of 103.74 yen touched in May.
MSCI's broadest index of Asia-Pacific shares outside Japan was slightly higher, though trading was cautious ahead of next week's U.S. Federal Reserve meeting.
Upbeat U.S. and Chinese data underpinned global stocks on Monday, while the slide in the yen spurred Japanese shares up over 2 percent. Nikkei futures were up slightly, indicating another positive session.
Signs of improvement in the global economy have provided fitful support to riskier assets in recent weeks as markets have been buffeted by uncertainty over the Fed's tapering timeline.
The euro was bolstered by rising short-term interest rates in the euro zone money market as chances of more easing by the European Central Bank faded, though analysts say the central bank's operations are likely to avert any credit crunch.
"Tensions in the liquidity market are set to remain until year-end," strategists at Barclays said in a note to clients. "But a 'liquidity accident' is unlikely as the full allotment at the ECB's operations is an important backstop," they added.
ECB Executive Board member Yves Mersch on Monday played down the prospect of asset purchases, saying such action poses immense challenges for the central bank.
The Fed is expected to begin tapering its own asset purchases in March, a Reuters poll showed on Monday, but some economists now say that it might do so as early as this month or next. The U.S. central bank will hold its next regular policy meeting on December 17-18.
By contrast, almost two-thirds of Japanese firms expect the Bank of Japan will increase its stimulus in the first six months of 2014, a Reuters poll showed on Tuesday, keeping pressure on the yen.
A spate of Fed officials on Monday also lent credence to the idea that a U.S. stimulus reduction was on the near-term horizon.
St. Louis Fed President James Bullard said the Fed could slightly reduce its monthly bond purchases this month in reaction to signs of an improved labour market, while Dallas Federal Reserve Bank President Richard Fisher said tapering should start next week. Meanwhile, Richmond Fed President Jeffrey Lacker said further stimulus is unlikely to do much to help the U.S. economy.
Bullard is a voting member of the policy-setting Federal Open Market Committee this year. He recently said a strong payrolls number would raise the chance of tapering in December, and the latest report released last Friday showed employers hired more workers than expected in November, driving the jobless rate to a five-year low of 7.0 percent.
On the commodities front, U.S. crude oil prices edged up to $97.39 per barrel, while Brent crude fell 2 percent on Monday in reaction to well-supplied markets and limited demand from European refiners.
