In Hong Kong, the Hang Seng index was around 0.2% higher, as of its final hour of trading, with shares of Chinese tech giant Tencent gaining 1.05%.

Mainland Chinese stocks were higher on the day, with the Shanghai composite gaining 0.61% to about 2,909.91 and the Shenzhen component adding 0.62% to 9,035.69. The Shenzhen composite rose 0.53% to around 1,541.65.

In South Korea, the Kospi gained 0.23% to close at 2,048.83. Over in Australia, the advanced 0.51% to finish its trading day Down Under at 6,484.80.

The Nikkei 225 in Japan added 0.37% to close at 21,260.14, while the Topix index rose 0.26% to finish the trading day at 1,550.99. Shares of semiconductor equipment manufacturer Tokyo Electron jumped 2.7% following the announcement of a share buyback, Reuters reported.

Shares in Asia were higher on Tuesday, as U.S. President Donald Trump concluded his state visit to Japan.

Trump ended his four-day state visit to Japan on Tuesday, a day after his news conference with Japanese Prime Minister Shinzo Abe, as the two countries seek to hash out a trade deal.

Trump said his goal was to remove trade barriers so as to give U.S. exports a fair footing in Japan, but he also described the U.S. trade imbalance with Japan as "unbelievably large" and expressed hopes to address that.

"The issues that America has with China, it also has ... in theory with Japan on tariffs although ... as you can see from what Trump is saying, he obviously feels closer to Japan," Hugh Young, head of Asia-Pacific at Aberdeen Standard Investments, told CNBC on Tuesday.

The U.S. president's visit to Japan comes amid a protracted trade war between Washington and Beijing, with China standing firm against the demands of the U.S. to change its state-run economy. Trump said Monday the U.S. is "not ready" to sign a deal with China yet.

"I think the market ... has already started to price in that the tension would be protracted," Eugenia Victorino, head of Asia strategy at SEB, told CNBC's "Street Signs" on Tuesday.

"I would expect that there is very little downside with respect to the dollar-Asian currencies at this point" unless the U.S. proceeds to impose higher tariffs on all Chinese exports, she said. "Having said that, we are still very much lacking growth in the region which would really not prop up the assets.

China's giant state-owned enterprises control strategic industries such as energy, telecommunications and defense. Since those companies benefit from favorable policies and subsidies, foreign companies complain of an unfair advantage. The escalating trade dispute between the U.S. and China has focused on allegations of the coerced surrender of proprietary technology and the trampling of intellectual property rights.

The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 97.777, after seeing a high of 97.836 earlier, but still off last week's levels of above 98.1.

The traded at 109.50 against the dollar after weakening from levels around 109.3 in the previous session. The changed hands at $0.6921 after touching an earlier low of $0.6914.

Oil prices were mixed in the afternoon of Asian trading hours, with the international benchmark Brent crude futures contract slipping 0.36% to $69.86 per barrel, while U.S. crude futures added 0.53% to $58.94 per barrel.

— Reuters and CNBC's Evelyn Cheng contributed to this report.