Earlier this week, US Federal Reserve chair Janet Yellen said the Fed should "proceed cautiously" before raising interest rates.
Wall Street was also spurred by the comments and saw its second day of gains on Wednesday.
The benchmark Nikkei 225 was up 0.41% to 16,943.48in early Thursday trade.
Tokyo-listed shares in Sharp were down 3.7% however after Taiwanese manufacturer Foxconn said it had finally agreed a deal to take over struggling Japanese electronics company.
Foxconn said the deal was worth 389bn yen ($3.5bn; Â£2.4bn) and would give it a 66% stake in Sharp.
In Australia, the benchmark S&P/ASX 200 index was up 1.56% to 5,088.7 points as the prospect of slower rate rises in the US buoyed investor sentiment.
Meanwhile, South Korea's benchmark Kospi index started in positive territory, but was later down 0.19% to 1,997.97.
Fresh official numbers released earlier showed industrial production in Asia's fourth largest economy had increased by 3.3% from a month earlier, marking the biggest monthly increase since late 2014.
In China, markets opened in positive territory despite some of the country's largest banks reporting lacklustre earnings growth late on Wednesday.
Profits for the Industrial & Commercial Bank of China (ICBC) and China Construction Bank both grew at less than half a percent. Industry-wide, nonperforming loans rose to 1.67% of total loans last year, up from the previous year.
Agricultural Bank of China, the country's third-largest lender, is expected to report its results later.
Hong Kong's Hang Seng index was up 0.11% to 20,831.47 in early trade, while the Shanghai Composite was up 0.28% to 3,008.98.
Markets in Asia were in positive territory early on Thursday as investors continued to find solace in Fed comments about US interest rates.