U.S. markets will be closed for the Memorial Day holiday.
Japan's Nikkei 225 index advanced 0.3% to 21,173.27 after visiting President Donald Trump said he expects a deal with Tokyo on trade after a Japanese election in July.
Trump has been seeking a bilateral trade deal with Japan after withdrawing from the Pacific Rim trading block, the Trans-Pacific Partnership. The two sides are working to close gaps over trade in farm products and autos and auto parts.
"We are working on the imbalance on the trade as there has been a tremendous imbalance so that we are working on that. And I am sure that will work out over a period of the time," Trump said. He said via Twitter that he expected an agreement in August.
Hong Kong's Hang Seng dropped 0.7% to 27,175.35 and the Kospi in South Korea fell 0.2% to 2,041.67 and the S&P ASX 200 edged 2.3 points lower to 6,453.70.
The Shanghai Composite index rose 0.3% to 2,860.50 and shares in Taiwan also were higher. Shares climbed in Jakarta and Thailand but fell in Singapore.
Without big data releases to drive sentiment, Trump's 4-day visit to Japan could enliven trading, said Jeffrey Halley of Oanda.
"We will almost certainly see some interesting 'comments' to drive volatility in Asia this week," he said in a commentary.
Stocks notched modest gains Friday on Wall Street, erasing some of the market's steep losses from a day earlier, but not enough for the market to avoid a third straight weekly loss.
Share benchmarks have swung between gains and losses as investors weigh the prospect of a prolonged trade war between the U.S. and China. Trading has been volatile since the dispute escalated earlier this month, with both sides raising tariffs on each other's goods.
Financial companies led Friday's buying as the yield on the 10-year Treasury note reversed part of a steep slide a day earlier. It was at 2.32% as of late Friday. Rising yields boost interest rates on loans, which makes lending more profitable.
The S&P 500 rose 0.1% to 2,826.06, ending the week with a 2.3% loss. The Dow Jones Industrial Average gained 0.4%, to 25,585.69. The Nasdaq composite added 0.1% to 7,637.01. Small company stocks fared better, and the Russell 2000 index climbed 0.9% to 1,514.11.
Investors will likely be stuck dealing with a volatile market until the outcome in the trade dispute becomes clear.
The 11th round of U.S.-China trade talks ended with no agreement. Instead, the U.S. moved to increase tariffs on Chinese goods, prompting China to reciprocate. The trade dispute escalated further after the U.S. proposed restrictions on technology sales to China.
President Donald Trump said Thursday that he expects to meet with his Chinese counterpart Xi Jinping at a summit next month in Japan. Both sides have expressed a willingness to resume negotiations, while at the same time ratcheting up antagonistic rhetoric, leaving investors confused about what happens next.
ENERGY: Benchmark U.S. crude lost 21 cents to $58.42 per barrel in electronic trading on the New York Mercantile Exchange. It climbed 1.7% to settle at $58.63 a barrel on Friday. Brent crude, the international standard, lost 1 cent to $67.46 per barrel. It gave up 3 cents to $67.47 per barrel on Friday.
CURRENCIES: The dollar rose to 109.46 Japanese yen from 109.31 yen on Friday. The euro strengthened to $1.1215 from $1.1190.
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