Mainland Chinese stocks dipped on the day, with the Shanghai composite down 0.23% to about 3,286.82 while the Shenzhen component shed 0.668% to around 13,466.85. Hong Kong's Hang Seng index slipped 0.69% to close at 24,710.59.
Over in Australia, the S&P/ASX 200 gained 0.74% to finish its trading day at 6,051.10.
Overall, the MSCI Asia ex-Japan index was little changed.
In a widely expected move, the Fed on Wednesday kept its benchmark overnight lending rate near zero.
"The focus now turns to the September meeting where the expectation is the Fed will provide more forward guidance," Tapas Strickland, director of economics at National Australia Bank, wrote in a note.
"I think the setting of policy now is probably is about as good as (the Fed) can do given the uncertainty around the path of the epidemic itself," Dennis Lockhart, former president of the Atlanta Federal Reserve, told CNBC's "Squawk Box" on Thursday.
"There's so much uncertainty around the virus, around … the public health question that I think they are in a situation where they really have to wait for a little bit more clarity before they can consider any more policy action," Lockhart said.
On the economic data front, Japanese retail sales for June declined 1.2% as compared to a year ago, according to a preliminary report by the country's Ministry of Economy, Trade and Industry. That compared against a median market forecast for a 6.5% year-on-year decline, according to Reuters.
Shares of Singapore banks tumbled on Thursday: DBS Group dropped 3.09% while Oversea-Chinese Banking Corporation fell 3.82% and United Overseas Bank slipped 3.15% The broader Straits Times index declined 1.7% to close at 2,529.82.
The moves came after the Monetary Authority of Singapore on Wednesday called on locally-incorporated banks headquartered in Singapore to "moderate" their dividends for fiscal year 2020.
"While the Local Banks' capital positions are strong, the dividend restrictions are a pre-emptive measure to bolster their resilience and capacity to support lending to businesses and individuals through an uncertain period ahead for our economy," the Singapore central bank said in a media release.
The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 93.55 after touching an earlier low of 93.31.
The Japanese yen traded at 105.01 per dollar following its strengthening earlier in the trading week from levels above 105.3 against the greenback. The Australian dollar changed hands at $0.714 after seeing an earlier high of $0.719.