Equities rose Thursday following a record lead from Wall Street, with investors cheered by hopes for a coronavirus vaccine and positive economic data offsetting fresh lockdowns.
Hong Kong led the gains on reopening after a one-day break, despite concerns about a new security law imposed on the city by China that observers said was more draconian than feared and could impact its future as an attractive business hub.
And while there are worries about the issue causing further friction between Beijing and the West, markets remain positive for now.
The Hang Seng Index rose almost three percent, while Shanghai ended up 2.1 percent.
In European midday deals, London grew 1.0 percent, Frankfurt jumped 2.1 percent and Paris gained 1.8 percent.
Tokyo though closed with a gain of only 0.1 percent, with signs of a flare-up in new cases in the Japanese capital weighing on sentiment.
Nevertheless there were advances across the board, which came after another all-time high Wednesday for the tech-heavy Nasdaq on Wall Street.
Investors were awaiting the release Thursday of key US June jobs data for a clearer idea on the economy following May's surprise jump in American employment.
There was some cheer as figures Wednesday from payroll services firm ADP showed a 2.37-million increase in private jobs -- slightly below forecasts -- though it added that 3.06 million posts were created in May, a revision from its initial report of 2.76 million lost.
Adding to signs that the worst of the economic hit may have passed, US factory activity began growing again.
Meanwhile, hopes for a vaccine were given a boost after Germany's BioNTech and US pharmaceutical giant Pfizer late Wednesday reported positive preliminary results from a joint project.
"Investors largely are shrugging off higher cases... as Pfizer reported positive results from a vaccine trial," said Neil Wilson at Markets.com.
"We have been here before -- it's too early to get too excited -- but a working vaccine is the holy grail as it would allow real normality to return to the economy."
Europe has continued with its lockdown easing, with the EU reopening its borders to visitors from 15 countries.
But the city of Leicester in central England has been put on a fresh lockdown after a spike in virus cases there, while experts said more UK cities and towns could follow.
There are increasing worries over a second wave of infections elsewhere, led by the United States, which on Wednesday reported more than 50,000 new cases for the first time and several US states imposed 14-day quarantines on visitors ahead of the July 4 weekend celebrations.
California suspended indoor dining at restaurants in Los Angeles and several counties, while New York scrapped plans to allow restaurants to seat customers inside from next week.
Apple has meanwhile closed another 30 US stores, half of them in California.
And the World Health Organization warned that with more than 10 million known infections worldwide and more than 500,000 deaths, the pandemic is "not even close to being over".
- Key figures around 1130 GMT -
London - FTSE 100: UP 1.0 percent at 6,220.58 points
Frankfurt - DAX 30: UP 2.1 percent at 12,511.31
Paris - CAC 40: UP 1.8 percent at 5,015.90
EURO STOXX 50: UP 2.0 percent at 3,292.49
Hong Kong - Hang Seng: UP 2.9 percent at 25,145.96 (close)
Tokyo - Nikkei 225: UP 0.1 percent at 22,145.96 (close)
Shanghai - Composite: UP 2.1 percent at 3,090.57 (close)
New York - Dow: DOWN 0.3 percent at 25,734.97 (close)
West Texas Intermediate: UP 0.8 percent at $40.14 per barrel
Brent North Sea crude: UP 0.9 percent at $42.41 per barrel
Euro/dollar: UP at $1.1281 from $1.1249 at 2100 GMT
Dollar/yen: UP at 107.47 yen from 107.43 yen
Pound/dollar: UP at $1.2500 from $1.2468
Euro/pound: UP at 90.25 pence from 90.19 yen