The stock rose on Thursday after a record Wall Street lead, with investors excited by the hope of a vaccine, more positive economic data and more blockages in Europe.
The developments helped to offset a worrying spike in infections in the United States, which led to the reimposition of containment measures that could slow recovery in the world's main economy and warn of worse.
Hong Kong led gains in the reopening after a one-day break, despite concerns over a new security law imposed on the city by China, which observers said was more draconian than feared and could impact its future as an attractive business center .
And while there are concerns about the problem causing further friction between Beijing and the West, markets remain positive for now.
The Hang Seng index rose more than two percent, while Shanghai finished 2.1 percent.
Sydney, Mumbai, Seoul, Wellington and Bangkok rose more than one percent, while Manila also recorded gains of more than two percent.
Taipei, Singapore and Jakarta were all in positive territory.
Tokyo ended 0.1% with signs of an outbreak in new cases in the Japanese capital weighing on sentiment.
London and Paris opened 0.7% more, while Frankfurt accumulated 1%.
The gains came after another historic Nasdaq rally on Wall Street, with investors awaiting the release of key US employment data in June later in the day, for better control of the economy after the May surprise jump in employment.
Payroll services firm ADP's numbers showed a 2.37 million increase in private jobs – slightly below forecasts – although it added that 3.06 million jobs were created in May, a review of its report 2.76 million lost.
Adding to the signs that the worst of the economic blow may be over, US manufacturing activity began to grow again, while the increase in German retail sales was four times more than expected in May.
Meanwhile, hopes for a vaccine have soared after Germany's BioNTech and US pharmaceutical giant Pfizer reported positive preliminary results from a joint project, which showed positive antibody responses.
Europe continued to ease the blockade, with the EU reopening its borders to visitors from 15 countries, while Spain and Portugal held a ceremony to release their land borders.
And the Netherlands confirmed the lifting of the measures imposed on its brothels and red light districts.
Europe opens, USA closes
"It was a positive risk start for the new quarter, starting with the old quarter, with more positive data surprises in the U.S. and encouraging news about the potential development of coronavirus vaccines," said Ray Attrill of the National Bank of Australia.
But he warned of a "need to be aware of the recent stoppage or even the reversal of restrictions on social distance in many US states, causing setbacks in some of these readings in the coming months".
There are growing concerns about the second wave of infections elsewhere, led by the United States, which on Wednesday registered more than 50,000 new cases for the first time and several US states imposed 14-day quarantines on visitors before the end celebrations. on the 4th of July.
California has suspended indoor dining at restaurants in Los Angeles and in several counties, while New York has scrapped plans to allow restaurants to accommodate customers within the next week.
Apple has announced that it will close another 30 American stores on Thursday, half of them in California.
And the World Health Organization has warned that, with more than 10 million infections known worldwide and more than 500,000 deaths, the pandemic "is not even close to ending".
"There is this inherent tension between the health of the economy and the health of the population," said David Lebovitz, strategist at JPMorgan Asset Management.
"It will be the way to think about what drives markets in the coming weeks or months."
– Key figures around 0720 GMT –
Hong Kong – Hang Seng: up 2.2% on 24,955.55
Tokyo – Nikkei 225: up 0.1 percent at 22,145.96 (close)
Shanghai – Composite: UP 2.1 percent at 3,090.57 (close)
London – FTSE 100: 0.7 percent rise on 6,201.10
West Texas Intermediate: UP 0.6 percent to $ 40.06 per barrel
Brent in the North Sea: up 0.6 percent to $ 42.30 a barrel
Euro / dollar: $ 1.1272 from $ 1.1249 at 2100 GMT
Dollar / yen: UP at 107.51 yen from 107.43 yen
Pound / Dollar: UP at $ 1.2492 from $ 1.2468
Euro / pound: UP at 90.23 pence from 90.19 yen
New York – Dow: LOW 0.3% at 25,734.97 (close)