Germany's DAX lost 0.1% to 12,924.33 while the CAC 40 in Paris also gave up 0.1%, to 5,723.26. Britain's FTSE 100 skidded 0.4% to 7,304.97. The future contract for the Dow Jones Industrial Average lost 0.1% to 27,018.00 and that for the S&P 500 declined 1.3 points to 3,035.00.
Shares rallied on Wall Street overnight, with the benchmark S&P 500 hitting a record high, at the onset of a week busy with corporate earnings and economic reports. Investors also are anticipating another interest rate cut by the Federal Reserve.
Investors have been balancing worries over the impact that the costly trade war between the U.S. and China is having on corporate profits and the global economy against renewed optimism that negotiations that got underway this month could result in some kind of resolution in the conflict.
"A U.S.-China trade deal, even an interim one, remains the critical macroeconomic event for the year," Jeffrey Halley of Oanda said in a commentary. "Number two is the trajectory of U.S. interest rates, and here the story is getting murky," he said.
In Asia, Japan's Nikkei 225 index gained 0.5% to 22,974.13, while the S&P ASX/200 edged 0.1% higher to 6,745.40. The Hang Seng in Hong Kong lost 0.4% to 26,786.76 and the Shanghai Composite index dropped 0.9% to 2,954.18.
Hong Kong's Chief Executive Carrie Lam said Tuesday that the city may fall into recession as it enters its fifth month of protests. Third quarter data are due for release on Thursday and if they show negative growth, then the semiautonomous Chinese territory's economy will have entered a technical recession.
In other markets, South Korea's Kospi was almost unchanged at 2,092.69. Shares rose in Taiwan and Singapore but fell in Bangkok and Jakarta. India's Sensex advanced 1.6% to 39,861.40. Traders are awaiting releases of several important U.S. economic reports this week, including the Labor Department's monthly employment report on Friday. Economists expect a slight increase in the unemployment rate to 3.6% in October from 3.5% in September.
The S&P 500 index closed Monday at 3,039.42, around 14 points above its previous record set on July 26 and up 0.6% for the day. It notched that milestone after weeks of hovering just below its prior high.
Investors have been encouraged as most of the companies that have reported quarterly results the past couple of weeks beat Wall Street analysts' forecasts for earnings growth. Despite Monday's rally, the market could be in for some volatility this week as some 156 companies in the S&P 500 are scheduled to issue their quarterly results this week.
While the market waits for something concrete to emerge from the U.S.-China trade negotiations, investors have been largely playing it safe. Benchmark crude oil lost 44 cents to $55.37 a barrel in electronic trading on the New York Mercantile Exchange. It fell 85 cents to settle at $55.81 a barrel on Monday.
Brent crude oil, the international standard, dropped 38 cents to close at $60.87 a barrel. The dollar fell to 108.92 Japanese yen from 108.96 yen on Monday. The euro weakened to $1.1081 from $1.1100.