Asian shares rose on Tuesday, with Japanese stocks hitting a 30-year high, as investor risk was encouraged by a Brexit trade deal and hopes a long-awaited U.S. pandemic relief package will be expanded.

MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.45 percent. Australian stocks ended up 0.53 percent. Japan's Nikkei surged by 2.4 percent to its highest since August 1990. Shares in China bucked the trend, falling 0.32 percent on profit taking.

Futures for the S&P 500 added 0.4 percent.

Euro Stoxx 50 futures were up 0.42 percent, German DAX futures rose 0.53 percent, and FTSE futures gained 1.12 percent, pointing to a bright start to European trade.

The U.S. dollar nursed losses against major currencies and Treasury yields rose after U.S. President Donald Trump's approval of a $2.3 trillion stimulus package to counter the effects of the coronavirus pandemic.

While the package still has to pass the Senate, Trump's approval on Sunday sent shares on Wall Street to record highs on Monday amid increased optimism about an economic recovery.

Jack Ma's Alibaba Group rose 6.4 percent, snapping six straight sessions of declines. Analysts said those gains could be shortlived given Chinese regulators have called for a shakeup of Ant Group, Alibaba's mobile payment and consumer finance arm.

Oil prices recovered after falling overnight because of concerns about increased supply and lower demand amid fresh COVID-19 travel restrictions around the world.

Brent crude rose 0.45 percent to $51.09 per barrel. U.S. crude was up 0.48 percent at $47.85 a barrel.

More U.S. fiscal stimulus has also eased concerns about the threat posed by new variants of the coronavirus identified in Britain and South Africa.

The yield on benchmark 10-year Treasury notes rose to 0.9381 percent, but the two-year eased to 0.1270 percent.

(Cover: A pedestrian looks at an electronic board displaying share prices of the Tokyo Stock Exchange, Tokyo, Japan, December 29, 2020. /CFP)