The Shanghai Composite index gained 1.7% to 3,243.91. Japan's Nikkei 225 index jumped 1.5% to 22,190.71 and the Kospi in South Korea added 0.7% to 2,249.43.
Hong Kong's Hang Seng picked up 1.1% to 30,245.00, while Australia's S&P ASX 200 lost 0.1% to 6,244.90. Stocks rose in Taiwan, Singapore and Indonesia but fell in the Philippines.
On Saturday, U.S. Treasury Secretary Steven Mnuchin told reporters that the U.S. and China were moving closer to an agreement on trade.
Speaking on the sidelines of the International Monetary Fund and World Bank spring meetings, Mnuchin said the U.S. and China had held phone discussions last week and he wasn't sure if more face-to-face meetings would be needed. He did not give a timeframe for when negotiations might be wrapped up.
Mnuchin added that the proposed agreement has seven chapters and will allow both countries to set up enforcement offices to make sure the deal is followed. This fueled hopes that a wide-ranging dispute between the world's two biggest economies could soon be put to rest.
Chinese foreign ministry spokesman Lu Kang said Thursday that the discussions were "moving forward" and "new substantial progress" was made.
"U.S. and China have been actively keeping alive hopes that a trade deal is within reach. This coupled with better-than-expected China data in March led the Shanghai Composite Index to its highest level since March 2018," DBS Group Research strategists Philip Wee and Joanne Goh said in a commentary.
Last week, China reported that its exports in March rose 14.2% from a year earlier. This was a turnaround from a 20.8% contraction in February, signaling stronger global demand. Sales to the American market also accelerated despite President Donald Trump's tariffs of up to 25% on $250 billion of Chinese goods.
On Wall Street, strong gains by banks on Friday led the broad S&P 500 index to its third straight weekly gain. It finished 0.7% higher at 2,907.41.
The Dow Jones Industrial Average rebounded 1% to 26,412.30 and the Nasdaq composite advanced 0.5%, to 7,984.16. The Russell 2000 index of smaller-company stocks was up 0.4% at 1,584.80.
ENERGY: Benchmark U.S. crude shed 24 cents to $63.65 per barrel in electronic trading on the New York Mercantile Exchange. The contract gained 31 cents to close at $63.89 on Friday. Brent crude, used to price international oils, lost 12 cents to $71.43 per barrel in London. It added 72 cents in the previous session to $71.55.
CURRENCY: The dollar weakened to 111.99 yen from 112.01 yen late Friday. The euro rose to $1.1315 from $1.1300.
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