The stock market in Australia, which has crucial economic links with China, rose 1.59%, while shares in China gained 0.72%.
Hong Kong stocks jumped 1.18%, undeterred by the Chinese parliament's passage of a security law that will increase Beijing's control over the former British colony.
The Nikkei rose 2%, shrugging off a larger-than-expected decline in Japanese industrial production.
Overall, however, Asian shares are still on course for a 7% decline over the first half of this year, underscoring the severity of the pandemic-sparked losses and the challenges facing investors as global infections continue to rise in a blow to hopes of a quick recovery.
"Overnight moves in markets were not large but one does get the distinct impression that markets have got it both ways – with equities rallying on rebounding data and bonds rallying on dismal COVID-19 news," said ANZ Research analyst Rahul Khare.
Indeed, for the second quarter Asia ex-Japan shares were on course for a 17.8% gain, which would be the biggest quarterly increase since the third quarter of 2009. Stocks appear to have received an added boost on Tuesday as some investors adjusted positions on the last trading day of the quarter.
On Monday, the Dow Jones Industrial Average rose 2.32%, the S&P 500 gained 1.47% and the Nasdaq Composite added 1.2%.
China's official purchasing managers' index (PMI) released Tuesday showed factory activity in the world's second-largest economy grew for a fourth straight month in June. China's services sector PMI also expanded at a faster pace compared to the previous month.
A recent resurgence in coronavirus infections had led some investors to question the strength of a rebound in global economic activity.
The swing in sentiment between hopes and fears has kept markets on edge.
The yield on benchmark 10-year Treasury notes was little changed at 0.6348% in Asia as traders braced for U.S. non-farm payrolls data on Thursday, which is forecast to show an improving labour market.
U.S. Federal Reserve Chairman Jerome Powell on Monday said the outlook for the world's biggest economy is "extraordinarily uncertain" and signalled more monetary stimulus may be necessary, which could limit gain in yields.
Confirmed COVID-19 cases worldwide rose past 10 million and deaths surpassed 500,000 on over the weekend.
The bulk of new cases were reported in the United States and Latin America, stoking fears that the outbreak could stall economic recoveries just as lockdowns begin to ease.
In currency markets, the dollar held onto gains against the yen and the Swiss franc as the recent increase in coronavirus infections supported safe-haven demand for the greenback.
In the onshore market, the yuan rose slightly to 7.0685 against the dollar.
U.S. crude CLc1 fell 0.48% to $39.51 a barrel, while Brent crude LCOc1 slipped 0.31% to $41.58 per barrel, weighed by concerns about oversupply after Libya cited progress in resuming oil exports.
(Additional reporting by Stanley White in Tokyo; Editing by Sam Holmes & Shri Navaratnam) ((email@example.com; +81 (0)3 4563 2799; twitter.com/stanleywhite1 ;))