France's CAC 40 lost nearly 0.2% in early trading to 5,981.59. Germany's DAX slipped 0.1% to 13,389.91, and Britain's FTSE 100 fell 0.1% to 7,509.62.
U.S. shares were set to drift higher with Dow futures little changed but inching up to 28,264. S&P 500 futures rose 0.1% to 3,200.40.
Markets got a big boost in confidence after the U.S. and China announced a long-awaited "Phase 1" trade deal.
The two sides agreed to cut tariffs on some of each others' goods and postpone other tariff threats, the first time the two countries have stepped back from the brink in their 17-month trade fight. In return, China promised to ramp up its purchases of U.S. agricultural, energy and other goods and to stop forcing U.S. companies to turn over technology as a condition of doing business in that country.
The trade pact alleviated some uncertainty, though many issues remain unresolved.
"As long as both sides continue to talk up the phase one agreement, then Santa may well deliver the end of December rally that every investor craves this time of year. We just have to hope that we're not getting overly excited about an exquisitely wrapped lump of coal," Craig Erlam of Oanda said in a commentary.
Stronger than forecast Chinese retail sales and factory activity in November have contributed to the festive mood.
In Asian trading, Japan's benchmark Nikkei 225 added 0.5% to finish at 24,066.12, while South Korea's Kospi gained 1.3% to 2,195.68. Hong Kong's Hang Seng added 1.1% to 27,805.60, and the Shanghai Composite stood at 3,022.42, up 1.3%. Australia's S&P/ASX 200 was little changed at 6,847.30.
Shares also rose in India and Taiwan, but fell in Thailand.
Overnight on Wall Street, the S&P 500 and Nasdaq notched all-time highs for the third straight trading day. The Dow Jones Industrial Average bested its last record high set in late November.
ENERGY: Benchmark U.S. crude rose 7 cents to $60.28 a barrel in electronic trading on the New York Mercantile Exchange. It rose 14 cents to $60.21 a barrel on Monday. Brent crude, used to price international oils, added 10 cents to $65.44.
CURRENCIES: The dollar rose to 109.58 Japanese yen from 109.54 yen on Monday. The euro weakened to $1.1139 from $1.1148.