Japanese markets were up 1.4%, Australian markets added 0.8% tracking strength in the global markets.
Asian share markets joined a global rebound on Wednesday as the immediate drag from the Brexit vote began to ebb and investors wagered central banks would ultimately ride to the rescue with more stimulus measures.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 1% to recoup around a third of Friday's stinging loss. Japan's Nikkei climbed 1.4%, while Australian stocks added 0.8%.
Any bounce was welcome, given global equity markets shed $3 trillion in value in the two days following Britain's shock vote, according to S&P Dow Jones Indices. Investors also pointed to solid US economic data as helping to steady the ship.
Yet Britain's course out of the EU remains unknown, leaving the future of the entire bloc and its currency an open question.
"The only certainty in Europe is uncertainty," said analysts as Australia and New Zealand Bank in a note.
"European leaders appear to want to move forward with Brexit plans as quickly as possible, but political turmoil within Britain suggests a quick turnaround is unlikely."
The unease was evident in sterling which slipped a third of a US cent over the morning to huddle at $1.3309, not far from the recent 31-year low of $1.3122.
The euro regained only a little ground to $1.1060, while the safe-haven yen steadied at 102.42 per dollar.
For now, investors are counting on central banks to step in with fresh stimulus to support markets over time.
Japanese Prime Minister Shinzo Abe urged the Bank of Japan to provide ample funds to ensure market liquidity.
In the first of Federal Reserve policymakers to comment since the vote, Governor Jerome Powell said it had shifted global risks "to the downside."
That only reinforced market expectations the Fed will no longer be able to hike US rates this year, and could even be forced to cut if the domestic economy falters.
YIELDING LESS THAN NOTHING
On Wall Street, the Dow rose 1.57%, while the S&P 500 gained 1.78% and the Nasdaq 2.12%. Badly beaten-down financials and tech stocks were among the top gaining sectors.
The calmer mood was reflected in the CBOE Volatility Index which fell about 21% on Tuesday to close to where it was before the vote. It was its largest one-day%age decline since August 2011.
Aiding sentiment were data showing the US economy grew at a 1.1% annualised rate in the first quarter, rather than the 0.8% pace reported last month.
Yet concerns about the impact of Brexit on global growth and all the talk that central banks might have to ease anew to offset it, kept sovereign bonds well supported.
Yields on US 10-year notes held at 1.47%, just above a near four-year low of 1.406% hit on Friday. Comparable German and Japanese bonds are into record territory and pay negative yields.
Indeed, all Japanese bonds out to 40 years now offer less than 0.1%, a nightmare for pension funds and insurers desperate for a "decent" return.
In commodity markets, gold stepped back after two heady days. Spot gold was holding at $1,319.40 an ounce, but off a low of $1,305.23.
Oil prices gained as a looming strike by Norwegian oil and gas field workers threatened to cut output. There were also reports oil producers and refiners in crisis-struck Venezuela were struggling to keep output up.
US crude oil futures were up 40 cents at $48.25, while Brent crude rose 27 cents to $48.85.
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