MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.2 percent, led by rebound in Australian shares .
Japan's Nikkei rose 1.3 percent to a 14-month high.
MSCI's broadest gauge of the world's stocks covering 46 countries rose nearly 1 percent to a record high, after posting its biggest daily gain in almost three months.
On Wall Street, the Dow Jones Industrial Average blasted through the 21,000-point mark for the first time. Both the Dow and the S&P 500 rallied around 1.4 percent.
The British pound sank to a six-week low of USD 1.2270 as disappointing UK economic data added to political nerves that have begun to weigh on the currency again after last year's Brexit vote.
Oil prices loitered within a familiar range, as record high US crude supplies tempered support from evidences that OPEC producers are complying with an agreement to cut production.
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