Market benchmarks in Shanghai, Tokyo and Hong Kong retreated.
Overnight, Wall Street's benchmark S&P 500 index rose 0.2% as gains for Facebook, Nvidia and other tech stocks offset losses for other industries.
Investors are swinging between optimism about a global economic recovery underpinned by coronavirus vaccinations and worry that central banks might feel pressure to withdraw stimulus to cool rising inflation pressures.
Traders are watching U.S. jobs data due out Friday for signs of whether the labor market “will start to show initial signs of heating” after the Federal Reserve said it might move up the target date for raising interest rates, Anderson Alves of ActivTrades said in a report.
Also Tuesday, the World Bank raised its forecast of China’s economic growth this year to 8.5% from its April prediction of 8.1%. The Washington-based lender said a full recovery requires progress in vaccinations against the coronavirus.
The Shanghai Composite Index fell 0.7% to 3,580.22 and the Nikkei 225 in Tokyo shed 0.9% to 28,791.20. The Hang Seng in Hong Kong lost 0.6% to 29,099.96.
The Kospi in Seoul retreated 0.4% to 3,289.17 and Sydney's S&P-ASX 200 lost 0.6% to 7,260.30.
On Wall Street, the S&P 500 rose to 4,290.61 while the Dow Jones Industrial Average dropped 0.4% to 34,283.27.
The Nasdaq composite added 1% to a record 14,500.51.
Nvidia jumped 5% after The Sunday Times in Britain reported several big customers of U.K. semiconductor company Arm came out in support of its proposed takeover by Nvidia.
Facebook climbed 4.2% after a federal judge dismissed antitrust lawsuits brought against it by the Federal Trade Commission and a group of state attorneys general. Apple rose 1.3%, Microsoft gained 1.4% and Intel climbed 2.8%.
Stock prices look expensive to some investors after rising faster than corporate profits. Inflation remains a worry, even if more investors have come around to the Federal Reserve’s view that it will be only a temporary problem.
Economists expect Friday's U.S. jobs numbers to show employers added 700,000 more than they cut in June. That would be an acceleration following a couple months of disappointingly slow hiring. They also expect the report to show that average hourly earnings jumped 3.7% in June from a year earlier.
A sharp rise in wages would be an even bigger worry about inflation for markets than the recent jump in commodity prices. Prices of oil, lumber and other commodities can rise and fall quickly, while wage gains tend to be more durable.
In energy markets, benchmark U.S. crude declined 39 cents to $72.52 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell $1.14 to $72.91 on Monday. Brent crude, used to price international oils, shed 46 cents to $73.68 per barrel in London.
The dollar declined to 110.51 yen from Monday's 110.55 yen. The euro retreated to $1.1913 from $1.1923.