In Japan, the Nikkei 225 finished near flat at 19,371.46, while across the Korean Strait, the Kospi was fractionally higher at 2,107.63. Hong Kong's Hang Seng index was off by 0.38 percent in afternoon trade, while Chinese mainland markets were mostly lower. The Shanghai composite closed down 10.13 points, or 0.31 percent, at 3,251.08 and the Shenzhen composite finished near flat at 1,991.98.
Australia's ASX 200 fell 20.43 points, or 0.35 percent, to 5,784.66, with gains in most sectors offset by a nearly 2 percent drop in the materials sector and a 2.03 percent decline in utilities.
Major miners in the country finished lower, with Rio Tinto down 5.45 percent, Fortescue off by 2.58 percent and BHP Billiton down 2.67 percent.
Nissan announced it was appointing its co-CEO, Hiroto Saikawa, to be the chief executive officer as of April 1. Carlos Ghosn, who is chairman of the board and current CEO, will continue to serve as chairman and will seek a renewal of mandate at Nissan's general shareholders meeting in June. Nissan shares slipped 0.58 percent.
Elsewhere, Reuters reported that South Korea's SK Hynix will consider making a fresh bid for Toshiba's flash memory chip business if the Japanese conglomerate offers more of it for sale.
On Wednesday, the Nikkei business daily reported that Toshiba asked potential bidders for the memory chip business to peg the unit's operations' value at 2 trillion yen ($17.6 billion) or more.
Toshiba shares closed down 4.32 percent, while SK Hynix fell 0.79 percent.
Analysts said the Fed's meeting minutes failed to give the dollar a lift that many had been waiting for.
Matt Simpson, senior market analyst at ThinkMarkets, said in a note the greenback "reconsidered breaking above 101.74 resistance, yet it's failure to do so for the second occasion in a week suggest potential for near-term weakness."
Simpson added in the absence of major data, unless there are further details on President Donald Trump's tax plans or fiscal stimulus, the dollar is expected to remain capped for the week.
Treasury Secretary Steve Mnuchin will appear on CNBC's "Squawk Box" at 7 a.m. ET Thursday, where traders are hoping he will reveal what the Trump administration's tax reform plan will look like — and when they might see it — among other details.
The yen traded at 113.25 to the dollar, strengthening from levels near 113.45, while the Australian dollar fetched $0.7686. The euro traded at $1.0554.
Eugenia Victorino, Asia economist at ANZ, said there is still room for further monetary easing from the Bank of Korea by the end of the second quarter.
"Overall growth is showing some signs of improvement on the back of a pick-up in exports," she said. "However, domestic demand remains soft ... (and) ... various indicators, aside from the gains in the CPI, suggest that underlying inflationary pressures are still weak."
The Korean won traded at 1,136.47 to the dollar, strengthening from levels near 1,141.70 earlier in the session.
Oil traded higher Thursday during Asian hours, with U.S. crude up 0.82 percent at $54.03 a barrel at 2:37 p.m. HK/SIN, while Brent climbed 0.82 percent to $56.30.
Data from the American Petroleum Institute on Wednesday showed crude inventories fell by 884,000 barrels in the week to Feb. 17 to 512.7 million, compared with analysts' expectations for an increase of 3.5 million barrels, Reuters reported.