The pan-European STOXX 600 reversed early losses to rise 0.1 percent at the close, while Germany's DAX, home to large exporters and carmakers, was down 0.2 percent.
Wall Street opened slightly lower but the dip did not change the mood across European bourses.
"I think the market has digested more or less all this rollercoaster with tariffs," said Dimitrios Stefanopoulos, portfolio manager at AlphaTrust in Athens, adding that investors believe Trump will seek a deal ahead of U.S. mid-term elections.
While the potential tariffs on China were reported to be lower than the 25 percent the administration had previously said it was considering, economists said this would still have a significant impact on markets.
"Our U.S. economists expect that even a 10 percent tariff rate will slow growth in Q4, resulting in the Fed skipping a December hike," wrote UBS strategists.
The market was buoyed by strong defensive telecoms and utilities stocks. Cyclicals sectors, which are more sensitive to trade and economic growth, have lagged as the trade war ramped up over the past months.
"If the trade war hits the economy, then defensives will be better off," Stefanopoulos said.
Several stocks shone after results on Monday, helping support risk appetite.
Forecast-beating sales from H&M sent the shares up 16.6 percent, an encouraging result for the world's second-biggest fashion retailer whose shares are still down a third of their value from a year ago.
The large amount of H&M shares being shorted by investors makes any positive news a significant boost for the stock as short sellers are "squeezed" to unravel their position.
Casino shares jumped 7.6 percent after the French supermarket's parent Rallye, through which Jean-Charles Naouri exercises control of the firm, got a new 500 million euro credit facility.
Rallye shares - which are highly shorted - jumped 13.8 percent.
Credit Suisse shares rose 0.6 percent after Swiss regulator Finma said the lender had failed in its duty to combat corruption in cases linked to FIFA and Venezuelan and Brazilian state oil companies.
The stock was likely supported by an interview with CEO Tidjane Thiam in Swiss newspaper NZZ am Sonntag, in which he said Credit Suisse was aiming for an annual profit of 5 to 6 billion francs for the next two years.
And on the M&A front, reinsurer Scor rose 1.5 percent after sources told Reuters unlisted French cooperative insurer Covea was working on a new approach for Scor after its friendly 8.2 billion euro offer was rejected last month.
(Reporting by Helen Reid,; Editing by Keith Weir and Ed Osmond)
By Helen Reid