Japan's Nikkei average was flat on the day but at its highest level in seven weeks. Australian shares jumped 2.2 percent, with long-battered financials surging on short-covering after a special government-appointed inquiry excoriated Australia's financial sector for misconduct but left the structure of the country's powerful banks in place.
Elsewhere in Asia, trade was light, with markets in greater China, Taiwan, South Korea, Singapore and Indonesia all closed for the Lunar New Year. On Wall Street, the S&P 500 gained, with technology and industrials the biggest winners as investors braced for another big week of fourth-quarter corporate earnings reports.
After the bell, Google operator Alphabet fell about 3 percent as its higher spending in the fourth-quarter worried investors even as its revenue and profits beat the Street's expectations. MSCI's gauge of stocks across the globe reached a two-month high, having risen more than 13 percent from its near two-year low late in December, helped by the Fed's change of tack.
Fed Chairman Jerome Powell has signalled its three-year tightening drive may be coming to an end amid a suddenly cloudy outlook for the U.S. economy due to global growth concerns and the U.S.-China trade dispute. The Fed said in a statement that Powell had told President Donald Trump and Treasury Secretary Steven Mnuchin late on Monday that "the path of policy will depend entirely on incoming economic information."
Data announced on Friday showed U.S. job growth surged in January while a key gauge of U.S. manufacturing sector showed surprising resilience after December's shocking fall, allaying fears the U.S. economy might be losing momentum quickly. Hiroshi Nakamura, senior manager of investment planning at Mitsui Life Insurance, said financial markets' positive reaction to the U.S. data is diminishing with time, but hopes for a U.S.-China trade deal "will continue to support markets until the two sides come to formal decisions".
The dollar was on a firm footing as investors continued to lap-up Friday's strong payrolls number and a manufacturing survey. The dollar's index against six major currencies was little changed at 95.833, having gained 0.27 percent on Monday.
The euro was also steady at $1.1436, off three-week high of $1.15405 set on Thursday. The greenback firmed to 109.98 yen, having risen to 110.165 overnight, its highest level in five weeks.
The British pound barely moved and was at $1.3038. On Monday, sterling quickly erased brief gains following a newspaper report that goods shipped to Britain from the European Union could be waved through without checks in the event of a "no-deal" Brexit.
The Australian dollar gained 0.3 percent to $0.7247 , erasing earlier losses, following the Reserve Bank of Australia left policy unchanged at its first meeting of this year but sounded less dovish than expected. Earlier on Tuesday, it fell as much as 0.5 percent after a slump in retail sales reinforced concerns about slowing growth in Australia.
In commodity markets, oil prices inched up, buoyed by expectations of tightening global supply amid U.S. sanctions on Venezuela and production cuts led by OPEC. U.S. West Texas Intermediate (WTI) crude futures rose 0.5 percent to $54.82 a barrel, after hitting a 2-1/2-month high of $55.75 in the previous session, while Brent crude futures were last up 0.4 percent at $62.77.
Gold prices held near one-week lows hit in the previous session, pressured by a firmer dollar and as investor appetite for riskier assets picked up. (Reporting by Hideyuki Sano & Tomo Uetake; Editing by Richard Borsuk,Shri Navaratnam & Kim Coghill)