Japan's Nikkei 225 index added 0.3% to 20,832.46 while the Shanghai Composite index lost 0.5% to 2,848.34. The benchmark in Shenzhen, a smaller, more domestic-oriented market, tumbled 1.5% to 1,471.73. Hong Kong's Hang Seng added 0.3% to 26,965.76 and Australia's S&P ASX 200 advanced 0.5% to 6,392.20. Shares fell in Taiwan and Singapore but rose in the Philippines. South Korean markets were closed for a holiday.
American and Mexican officials said late Wednesday that progress was being made at immigration talks at the White House, but President Donald Trump tweeted that it was "not nearly enough."
Trump, who was visiting Ireland, said talks would resume Thursday "with the understanding that, if no agreement is reached, Tariffs at the 5% level will begin on Monday, with monthly increases as per schedule."
It is unclear how the U.S. will gauge that Mexico has successfully stemmed the migrant flow from Central America. The Department of Homeland Security announced separately that border arrests reached 132,887 in May, the highest level in more than a decade.
In other news, the U.S. and China concluded their 11th round of trade talks last month with no agreement. No further talks have been arranged.
On Wall Street, broad gains by technology, industrial and health care companies lifted indexes Wednesday. Traders paid little attention to a report showing that private U.S. companies added the fewest jobs in nine years last month. The report may have been seen as positive in that it might encourage the Federal Reserve to cut interest rates.
The S&P 500 index gained 0.8% to 2,826.15 and the Dow Jones Industrial Average jumped 0.8% to 25,539.57. The Nasdaq composite rose 0.6% to 7,575.48. But the Russell 2000 index of smaller company slipped 0.1% to 1,506.79.
ENERGY: Benchmark U.S. crude picked up 14 cents to $51.82 per barrel in electronic trading on the New York Mercantile Exchange. It gave up $1.80 to settle at $51.68 a barrel on Wednesday. Brent crude oil, the international standard, added 18 cents to $60.81 per barrel. The contract shed $1.34 to $60.63 per barrel in the previous session.
CURRENCIES: The dollar slipped to 108.22 Japanese yen from 108.46 yen late Wednesday. The euro strengthened to $1.1231 from $1.1221.
AP Business writers Damian J. Troise and Alex Veiga contributed.