Shanghai, Tokyo, Hong Kong and Sydney declined.
Wall Street's benchmark S&P 500 index closed lower, weighed down by declines for tech, energy, industrial and communications stocks.
Investors were encouraged by unexpectedly strong U.S. earnings but are more uneasy as China, the United States and other governments try to stop the spread of the more contagious delta variant.
“It is clear that COVID delta variant risks have not been put to bed,” said Mizuho Bank in a report.
The Shanghai Composite Index lost 0.6% to 3,444.12 and the Nikkei 225 in Tokyo sank 0.9% to 27,538.50. The Hang Seng in Hong Kong tumbled 1.5% to 25,849.38.
The Kospi in South Korea retreated 0.2% to 3,215.30 and Sydney's S&P-ASX 200 was 0.4% lower at 7,463.50.
New Zealand, Bangkok and Indonesia gained while Singapore retreated.
Investors looked ahead to U.S. employment data due out Friday for indications of whether hiring has held up.
On Thursday, U.S. markets appeared to shrug off a report by the Institute for Supply Management, a trade group of purchasing managers, that manufacturing slowed in July. Many companies are being held back by supply chain disruptions.
The S&P 500 slipped 0.2% to 4,387.16. The index is coming off a weekly loss but is within 0.8% of its all-time set a week ago.
The Dow Jones Industrial Average dropped 0.3% to 34,838.16. The Nasdaq composite added 0.1% to 14,681.07.
A slide in technology, industrial, raw materials and communication companies weighed on the market. Energy stocks also fell in tandem with crude oil prices. Gains by health care stocks, utilities and a variety of retailers and other companies that rely on direct consumer spending helped keep the losses in check.
Also this week, some 150 companies in the S&P 500 are due to report results.
In energy markets, benchmark U.S. crude lost 1 cent to $71.25 per barrel in electronic trading on the New York Mercantile Exchange. On Monday, the contract fell $2.69 to $71.26. Brent crude, the price basis for international oils, shed 3 cents to $72.86 per barrel in London. It tumbled $2.52 the previous session to $72.89 a barrel.
The dollar declined to 109.22 yen from Monday's 109.25 yen The euro was little-changed at $1.1873.