Japanese shares led the way in Asia, with the Nikkei rallying 3.1%. South Korea stocks rose 0.7%, Australia put on 1.6% and Chinese stocks up 0.8%.
"Last week's FOMC meeting was a hawkish surprise, but does not change our market outlook. The reflation trade experienced a sharp technically driven pullback, but we expect the trade to resume and see this move as an opportunity to add exposure to cyclical equities and commodities," JPMorgan strategists said in a note.
Investors are keenly focused on the U.S. labour market as its performance is likely to have an influence on the Fed's policy stance. In the immediate hours ahead, all eyes are on Fed chief Jerome Powell who appears before Congress from 1800 GMT.
The U.S. Federal Reserve sent global stock markets skidding last week by signalling it would raise interest rates at a faster pace than previously expected, and also flagged its intention to consider withdrawing its monetary stimulus moving forward. Most Fed officials moved their projections for the first rate increases from 2024 to 2023, though some saw rates moving higher next year.
The Fed's pivot toward starting policy normalisation was driven by rapidly rising inflation, a dynamic that has kept financial markets on edge in the past few months.
Tuesday's momentum in Asian equities was underpinned by a rally on Wall Street, with the Dow registering its strongest session in more than three months.
On Monday, Fed officials including as St. Louis Fed President James Bullard and Dallas Fed President Robert Kaplan toned down their hawkish rhetoric.
In currency markets, the dollar paused for breath after gaining sharply in the wake of the Fed's policy surprise.
"The whole world was mega short the U.S. dollar, and that's in good part has probably been cleaned out already, and now we take a wee breath before the next move up," said Westpac currency analyst Imre Speizer.
Against the euro, the dollar nursed overnight losses of about 0.4% to hold steady around $1.1905. It held at 110.26 yen, and the dollar index was little changed at 91.96 after giving up about 0.5% on Monday.
Bitcoin stabilised in Asian trading and was last up 4.1% at $32,941. Bitcoin and other cryptocurrencies had come in for heavy selling on Monday, hurt by a tightening crackdown on trading and mining in China.
Benchmark 10-year U.S. Treasury notes last fell 3/32 in price to yield 1.4954%.
U.S. crude was flat at $73.7 per barrel and Brent edged up 0.32% to $75.1, after ring on Monday in reaction the a pause in talks to end U.S. sanctions on Iranian crude. Oil market sentiment was helped by hopes for a quick recovery in oil demand in the Unitedd States and Europe. Spot gold added 0.3% to $1,787.61 an ounce.
(Reporting by Anshuman Daga; Additional reporting by Tom Westbrook; Editing by Simon Cameron-Moore) ((email@example.com;))