Japan's Nikkei 225 rose 85.58 points, or 0.39 percent, to 22,262.6 while the Topix index added 5.81 points, or 0.35 percent, to 1,659.47. South Korea's Kospi was higher by 5.88 points, or 0.28 percent, to 2,114.1.
Greater China markets lost their early momentum and declined in the afternoon: The Shanghai composite gave up gains to close down 34.29 points, or 1.32 percent, at 2,567.44 while the Shenzhen composite was off by 29.94 points, or 2.2 percent, to 1,325.43. Hong Kong's Hang Seng index fell 0.93 percent in late afternoon trade.
In Australia, the ASX 200 added 33.3 points, or 0.58 percent, to 5,758.4, with advances in most sectors. The energy subindex was up 0.1 percent, materials was higher by 1.33 percent and the heavily weighed financial sector added 0.54 percent.
The session in Asia followed a major rally on Wall Street, where the Dow Jones industrial average jumped more than 600 points.
Stock market reaction in the U.S. was spurred by remarks from Federal Reserve Chairman Jerome Powell. He said Wednesday that he considers the central bank's benchmark interest rate to be near a neutral level, an important distinction from remarks he made less than two months ago.
"Considering that there's been no interest rate hikes since September, these comments tell us one of two things, which is that the Fed has finally figured out where the neutral rate is or they believe that a pause in tightening has become necessary," Kathy Lien, managing director of foreign-exchange strategy at BK Asset Management, wrote in an evening note on Wednesday.
"Chances are it's the latter because economic data has been weakening, stocks have been falling and lower oil and gas prices restrict rather than encourage inflation," she said.
Powell's comments pushed the U.S. dollar lower against a basket of its peers, with the dollar index trading at 96.704 Thursday afternoon, down from levels above 97.200 overnight.
Lien also pointed out that it was important to realize while Powell's remarks "could be a game changer" for the dollar, external factors that are driving other currencies lower have not changed.
Still, worries and uncertainties remain, according to other market watchers.
"Market sentiment had been a little more positive before Powell's speech, but trade uncertainty continues to weigh," Jack Chambers from ANZ Research wrote in a morning note. "Investors will be looking for progress at the Trump-Xi meeting this weekend, after it was reported that President Trump is weighing up more tariffs."
Top White House economic advisor Larry Kudlow said earlier this week that the Trump administration has restarted talks with the Chinese government "at all levels" ahead of the high-stakes meeting between both presidents at the G-20 summit in Argentina.
During the meeting, Trump is set to focus on issues including alleged Chinese theft of intellectual property, ownership of American companies in China and tariffs and non-tariff barriers.
Analysts from Citi Research said that the "base case" for the Trump-Xi meeting is that both countries would announce a "vaguely worded deal that shall put additional tariffs off the table." But, they added, the additional increase of tariffs to 25 percent on $200 billion of Chinese exports in January may not be discussed.
In the broader currency market, the yen traded at 113.29 to the dollar while the Australian dollar was around $0.7316, jumping from levels below $0.7250.