European shares were set to open slightly lower, according to financial spreadbetters, while U.S. equity futures were virtually flat.
The dollar <.DXY> dropped 0.4 percent against a basket of major currencies, extending Monday's slide after upbeat manufacturing data from the United States, India and China bolstered optimism about a global recovery and encouraged buying of higher-yielding currencies, commodities and stocks.
Investors are seeking more risks thanks to better economic conditions, said Tsutomu Soma, senior manager of foreign securities at Okasan Securities in Tokyo.
However, he said the optimism could change if U.S. job data due on Friday disappoints.
Investors feel they need to have the employment data to confirm the U.S. economy is improving solidly, Soma said.
Japan's Nikkei share index <.N225> rose 0.25 percent on the day to close at a 15-month high, helped by resource-related shares after the price of copper, palladium and platinum surged on Monday to their highest levels since 2008.
However, stocks came off earlier highs as a stronger yen hurt exporters.
The MSCI index of Asia Pacific stocks traded outside Japan <.MIAPJ0000PUS>, which rallied about 68 percent last year, was up 1.3 percent at levels last seen in July 2008.
Investors poured a record $19 billion into Asia ex-Japan equity funds last year, global fund tracker EPFR said on Tuesday, as the region led a recovery in the global economy.
A string of bullish data from China, India and South Korea since the start of this year is encouraging investors to add exposure to Asian assets, although uncertainty about the sustainability of economic recovery in Western economies poses a risk for equities globally, analysts say.
The strength of commodity prices lifted stocks in resource-rich Australia, where mining stocks helped drive the benchmark S&P/ASX 200 index <.AXJ0> up 1 percent.
The Thomson Reuters index of Asian shares outside of Japan <.TRXFLDAXPU> rose 1 percent.
OIL NEARS $82
A rally in U.S. shares on Monday boosted investment sentiment in Asia, which relies heavily on U.S. end demand for its exports industries.
U.S. stocks rallied on their first trading day of 2010 after the Institute for Supply Management manufacturing index for December hit its highest level since April 2006.
However, the economic recovery in the United States, as well as in Europe, was tepid and so could limit the upside potential of equities, said David Spry, research manager at FW Holst in Australia.
I don't think we're going to get a strong, sustained upswing until those economies start to contribute a bit more down the track, Spry said.
Uncertainty about Friday's U.S. jobs report for December capped buying of U.S. Treasuries in Asia. The November report showed a surprisingly small drop in jobs so further signs of an improving labor market in this week's report could trigger expectations for an early rise in U.S. interest rates.
The median forecast in a Reuters poll was for the report to show a fall of 8,000 jobs in December.
Benchmark 10-year treasuries rose 5/32 in price to yield 3.798 percent, down 2 basis points from late New York trade on Monday.
With risk appetite growing once again, higher-yielding and emerging-market assets benefited. Investors bought into the high-yielding Australian dollar, which hit a three-week peak at $0.9164 to the dollar.
In Korea, foreign exchange authorities were spotted intervening to stem the won as it rallied 1.3 percent against the dollar, its biggest daily gain since July last year.
Expectations that the central bank could soon raise interest rates are helping drive the currency higher following a string of bullish data on Asia's fourth-largest economy. Only Australia in the G20 has raised rates so far following the global financial crisis.
Exceptionally cold weather in the United States and other big consuming nations pushed oil prices up for a ninth straight session to near $82 a barrel, a sharp increase from below $70 in mid December.
The fall in the dollar is drawing buyers back to gold, which rose in Asia to $1,125.10 an ounce, its highest level since December 17. A fall in the dollar makes gold cheaper for investors using other currencies.
Reflecting its inverse relationship with the dollar, the precious metal dropped 7 percent in December as the dollar rallied 4 percent against major currencies.
(Additional reporting by Sonali Paul in MELBOURNE and Rika Otsuka in TOKYO; Editing by Neil Fullick)