After initially falling 1% in early trade, the benchmark Nikkei 225 was up 0.72% to 16,138.48 by late morning.
Analysts said the early morning falls were due to investors taking profits after the steep hikes a day earlier.
Shares in Japan's telecoms giant Softbank Group rose as much as 14% in early trade.
The firm announced its biggest share buyback to-date in an attempt to shore up investor sentiment following a sharp fall in its latest quarterly profits.
In China, markets rose, despite disappointing trade number released from the government on Monday.
The Shanghai Composite was up 2% to 2,801.17 points, while Hong Kong's Hang Seng index was up 1.5% to 19,201.96.
Monday's comments from the head of China's central bank, Zhou Xiaochuan, aimed at easing concerns about falls in the country's currency reserves, saw the onshore yuan in its biggest daily rise since 2005 when the country dropped an official peg to the dollar.
The onshore yuan is traded only in China and is controlled by Beijing. The offshore yuan is free of Beijing's control.
"Trade balance was weak, and the export figures illustrate demand isn't there on a global basis," said Evan Lucas from IG Markets.
"However, the Zhou effect cannot be ignored and the CNY [onshore yuan] fix coupled with his comments should settle the fear factor around an August 2015-styled devaluation."
Elsewhere, South Korea's benchmark Kospi index was up 1.1% in line with regional sentiment - to 1,882.44 points. The country's central bank left its rates unchanged at a record low of 1.5%, which was widely expected.
After falling earlier, Australia's benchmark S&P/ASX 200 index had also moved slightly higher to be up 0.1% to 4,848.20 points.
BBC