Asian shares surged on Tuesday, following a raft of good news — U.S. stocks recovered overnight and the pound jumped as British Prime Minister Theresa May managed to secure last-minute support from the EU for her Brexit deal before it goes to a crucial vote on Tuesday.

MSCI's broadest index of Asia-Pacific shares outside Japan pared some gains to rise 0.9 percent in the afternoon. Oil stocks in Asia bounced strongly as crude prices continued to recover this week, lifted by comments from Saudi Energy Minister Khalid al-Falih who said that an end to OPEC-led supply cuts was unlikely before June.

U.S. crude rose 0.28 percent on Tuesday afternoon to settle at $56.96, while the international benchmark Brent was up 0.15 percent to $66.66 a barrel.

In Japan, the Nikkei 225 rose 1.79 percent to close at 21,503.69, after surging past 2 percent earlier. The broader Topix rose 1.52 percent to finish at 1,605.48.

The Shanghai composite jumped over 1 percent to close at 3,060.31, while the Shenzhen composite bounced 1.67 percent to finish at 1,695.80. Hong Kong's Hang Seng index traded up 1.44 percent during the final hours of the trading day.

Shares of China's Meituan Dianping, an online food delivery-to-ticketing firm, plunged more than 10 percent by the afternoon, following results posted a day earlier which showed that its fourth-quarter operating loss more than doubled.

South Korea's Kospi traded higher by 0.89 percent to close at 2,157.18.

In Australia, the rose earlier but declined 0.09 percent to close at 6,174.80. Oil stocks put in a strong showing in the afternoon after losses on Monday, with shares of Santos surging 2.79 percent, Oil Search giving up some gains to rise 0.51 percent, and Woodside Petroleum rising 1.12 percent.