France's CAC 40 was up 0.6% to 5,611, while Germany's DAX was 0.4% higher at 12,432. Britain's FTSE 100 gained 0.5% to 7,566.
U.S. shares looked set for small gains, with the future contract for the Dow Jones Industrial Average up 0.1% and the S&P 500 futures rising less than 0.1%.
Banks Wells Fargo and Goldman Sachs reported second quarter results that beat estimates, pushing up shares in pre-trading.
Pharmaceuticals and consumer goods maker Johnson & Johnson posted slightly lower sales across much of its business in the second quarter, but its profit figure was higher than analysts were forecasting.
The numbers are likely to be reassuring to investors worried about a slowdown in economic growth and the looming impact of the impasse between the U.S. and China over trade.
The White House's repeated threats to raise tariffs further in retaliation for the U.S. trade deficit and policies that critics say are unfair has made companies hesitant to invest and has hurt trade internationally. They're a big reason China on Monday reported its weakest quarter of economic growth in at least 26 years.
U.S. Treasury Secretary Stephen Mnuchin told reporters in Washington on Monday that he has held "several conversations" with Chinese officials and expects another phone call this week.
The aim is to restart high-level talks that collapsed in May.
"To the extent that we make significant progress I think we'll go there," he said.
In Asian trading, Japan's benchmark Nikkei 225 declined 0.7% to finish at 21,535.25. Australia's S&P/ASX 200 lost nearly 0.2% to 6,641.00. South Korea's Kospi added 0.5% to 2,091.87 and Hong Kong's Hang Seng rose 0.2% to 28,619.62, while the Shanghai Composite shed 0.2% to 2,937.62.
Shares have jumped since early June on increasing expectations that the U.S. Federal Reserve will cut interest rates to help the economy, and investors are virtually certain that it will happen at the next Fed meeting at the end of this month. The only question, investors say, is how deeply the Fed will cut when it lowers rates for the first time in a decade.
ENERGY: Benchmark U.S. crude fell 2 cents at $59.56 a barrel. It fell 63 cents on Monday. Brent crude, the international standard, shed 4 cents to $66.44 a barrel.
CURRENCIES: The dollar rose to 108.01 Japanese yen from 107.98 late Monday. The euro fell to $1.1221 from $1.1258.