Japan's Nikkei 225 jumped 2.61 percent to close at 20,864.21, while the Topix gained 2.16 percent to finish its trading day at 1,572.60. Shares of Fast Retailing rose 3.01 percent while chip company Renesas Electronics skyrocketed 16.26 percent.
Mainland Chinese markets were higher in the day. The Shenzhen component rose 1.149 percent to close at 8,010.07 while the Shenzhen composite advanced 1.203 percent to finish its trading day at 1,364.15. The Shanghai composite also went up 0.68 percent to close at 2,671.89.
Hong Kong's Hang Seng index was largely flat, as of its final hour of trading.
South Korea's Kospi gained 0.45 percent to close at 2,190.47, as shares of industry heavyweight Samsung Electronics and chipmaker SK Hynix jumped 2.33 percent and 2.43 percent, respectively. LG Electronics gained 3.75 percent.
The ASX 200 in Australia recovered from its earlier dip to close 0.3 percent higher at 6,079.10 as the sectors mostly rose. The energy subindex gained 1.22 percent as shares of oil companies advanced. Santos was up 1.89 percent, Woodside Petroleum advanced 0.58 percent and Beach Energy rose 2.11 percent.
Looming US-China trade talks weigh
"I think the most likely scenario is a deal with no more tariffs being imposed going forward," David Cui, head of China equity strategy at Bank of America Merrill Lynch, told CNBC's "Street Signs" on Tuesday.
"There's a possibility they keep existing tariffs imposed last year for a while to monitor performance, but I think (it is) highly unlikely there will be more tariffs imposed. It's also possible to delay the negotiation for a couple of more months to nail down some of the details. I think the least likely scenario is a ... complete breakdown of the negotiation," he added.
Currencies and oil
The Japanese yen traded at 110.49 against the dollar after seeing an earlier low of 110.64. The Australian dollar was at $0.7084 after touching an earlier low of $0.751.
Oil prices gained in the afternoon of Asian trade. The international benchmark Brent crude futures contract rose 0.47 percent to $61.80 per barrel. U.S. crude futures advanced 0.34 percent to $52.59 per barrel.
— Reuters and CNBC's Fred Imbert contributed to this report.