Japan's Nikkei Stock Average surged 1.6% after closing at its highest level since April on Wednesday, while South Korea's Kospi rose 0.4%, and Australia's S&P/ASX 200 index edged up 0.1% after reaching its best level for around 17 months on Wednesday.
Hong Kong's Hang Seng Index rose 0.2% to extend highs not seen since mid-2011, although the Shanghai Composite Index bucked the regional gains to slip 0.4%, paring its month-to-date advance to just under 5%.
In U.S. trading overnight, the Dow Jones Industrial Average (DJI) and S&P 500 (SPX) ended little changed, after Federal Reserve Chairman Ben Bernanke warned that the Fed does not have the ability to shield the economy from the fiscal cliff of large potential tax hikes and spending cuts.
The U.S. central bank chief made the comments at a news conference Wednesday to discuss the Fed's newly announced plan to expand its asset-buying program and to hold rates close to zero until unemployment falls below 6.5% or until inflation accelerates.
"[Asia] sentiment has been boosted by the Fed's confirmation of outright purchase of long-dated Treasurys, which translates into a bigger asset-purchase program," said Frances Cheung, strategist at Credit Agricole.
"Flows into Asian markets are likely to continue," she said.
An important after-effect from the Fed meeting for Asian investors was a sharp climb in the dollar against the Japanese yen.
In overnight trading, the dollar (USDJPY) shot above the �83 mark for the first time since April 2, after sitting in the low �82 range the previous day.
While the move partly stemmed from a steeper Treasury curve, according to BNP Paribas currency strategists, "at the same time markets remain clearly focused on the Bank of Japan's policy" ahead of Japanese leadership elections this weekend, they said.
The currency move spurred fresh gains for Japan's exporters, with technology firms and auto makers among the best-performing sectors Thursday.
Advantest Corp. (ATE) rose 5.4%, TDK Corp. (TTDKF) added 4.6%, Canon Inc. (CAJ) improved by 3.1%, Pioneer Corp. (PNCOY) rallied 3.8% and Panasonic Corp. (PC) gained 6.5%.
Mazda Motor Corp. (MMTOY) drove 5.2% higher, and Honda Motor Co. (HMC) advanced 1.9% despite its Canadian unit announcing a recall of some vehicles.
Japanese banks also got an uplift, with Sumitomo Mitsui Financial Group Inc. (SMFJY) rising 2.7%, and Nomura Holdings Inc. (NMR) ahead by 3.4%.
Over in Hong Kong, transport firms saw some share-price strength, with ports operator Cosco Pacific Ltd. and airline Cathay Pacific Airways Ltd. each rising 1.6%.
Aluminium Corp. of China Ltd. (ACH) advanced 1.7% in Hong Kong, but fell 0.6% in Shanghai, while PetroChina Co. (PTR) was flat in Hong Kong but down 0.7% in Shanghai.
South Korean shares got support from gains for technology companies, with Samsung Electronics Co. (SSNLF) extending its recent all-time highs with another 1.7% rise Thursday.
In Australian trading, retailers gained, with Super Retail Group Ltd. up 2.3%, and Harvey Norman Holdings Ltd. rallying 3.3%.