Japanese shares led gains among major markets in the region, with the Nikkei 225 up 2.55% to close at 21,271.17 as shares of index heavyweight and conglomerate Softbank Group jumped 4.3%. The Topix index also ended its trading day 2.17% higher at 1,534.73. The moves came after Japan's Prime Minister Shinzo Abe announced Monday that the state of emergency will be lifted in the last five of the country's 47 prefactures, according to state broadcaster NHK.
Hong Kong's Hang Seng index also saw robust gains, rising 2.08%, as of its final hour of trading. Mainland Chinese stocks advanced on the day, with the Shanghai composite up 1.01% to about 2,846.55 while the Shenzhen composite soared 2.21% to around 1,789.52.
South Korea's Kospi also gained 1.76% to close at 2,029.78 as shares of LG Chem surged more than 6%. Meanwhile, shares in Australia jumped, with the S&P/ASX 200 up 2.93% to finish its trading day at 5,780.
Overall, the MSCI Asia ex-Japan index rose 1.86%.
Investors watched for market reaction to the announcement from Novavax, where the firm said it expects initial results on safety and immune responses in July. That comes on the back of Moderna's recent report of a positive development in its vaccine trial where all 45 participants had developed coronavirus antibodies.
Globally, more than 5.4 million people have been infected by the coronavirus so far while at least 344,000 lives have been taken, according to data compiled by Johns Hopkins University.
JPMorgan Asset Management's Kerry Craig told CNBC's "Squawk Box" on Tuesday that the market's focus has shifted "from thinking about the viral risk to think about the political risk" in recent days as U.S.-China tensions reignite.
"As more economies open up, as we see more business surveys, consumer surveys and economic data point to April being the low. You have seen the markets start to recover, look at that light at the … end of the tunnel and then think about better prospects for the markets," said Craig, who is global market strategist at the firm. That has resulted in markets moving higher despite a "re-invigoration" of political risk, particularly between the U.S. and China, he added.
"Political risk is gonna be with us for some time, it's gonna add to that market volatility, it really is a case of how much investors are gonna be desensitized to it and rather focusing on the improving economic outlook that comes through and the potential for gains as we enter this new cycle … and the long run return for equities could be potentially possible," said Craig.
In economic news, Singapore cut its 2020 economic forecasts for the third time this year. The Singapore economy is now expected to shrink by between 4.0% and 7.0% this year, according to the country's Ministry of Trade and Industry.
The U.S. dollar index, which tracks the greenback against a basket of its peers, last traded at 99.575 after declining from levels above 100 last week.
The Japanese yen traded at 107.85 per dollar following a weakening from levels below 107.2 in the previous trading week. The Australian dollar changed hands at $0.6588 after dipping from highs above $0.658 seen last week.
Oil prices were higher in the afternoon of Asian trading hours, with international benchmark Brent crude futures up 2.45% to $36.40 per barrel. U.S. crude futures also gained 3.73% to $34.49 per barrel.
— CNBC's Yun Li contributed to this report.