The pan-European STOXX 600 index <.STOXX> rose 0.4% in muted volumes, adding to its 0.8% rise on Monday after the United States and China agreed to return to the negotiating table after a breakdown in trade talks in May.
Europe's main indexes had a subdued start on Tuesday as investors turned sceptical about a U.S.-China trade deal after Trump said any trade deal with China would need to be "somewhat tilted" in favour of the United States.
Offering little respite, the U.S. government on Monday ratcheted up pressure on Europe by releasing a list of additional products - including olives, Italian cheese and Scotch whiskey - that could be hit with tariffs.
Trade-sensitive German shares <.GDAXI> underperformed. But investors largely seemed to have digested the news already, with the food and beverage index <.SX3P> among the top gainers, up 1.2%.
"EU tariffs are just a comment, not any actuality," Keith Temperton at Tavira Securities said.
"So for now it's fairly unimportant and tiny anyway," Temperton said, adding the additional tariffs would be "a drop in the ocean."
Planemaker Airbus, however, fell 0.3% as further tariff threats become the latest salvo in a long-running dispute over aircraft subsidies.
The STOXX 600 index had its worst performance in more than two years in May after a sudden escalation in U.S.-China trade tensions.
But stocks recouped most of their losses since then on hopes that major central banks would be more accommodative to counter the impact of the dispute. Developments on the trade front and central bank follow through will determine if July can maintain the momentum.
Utility stocks <.SX6P> which tend to fare better in a falling interest rate environment rose 1.9% on Tuesday, with Italian firms Italgas Terna and Hera up between 2.2% and 3.5% as 10-year government bond yields fell below 2%.
Milan's main index <.FTMIB> rose 0.7% with data showing that 2019 budget deficit was smaller than forecast.
This assuaged investor concerns as it meant the country probably complied with European Union fiscal rules this year and could possibly avoid disciplinary action over its growing debt.
Galapagos jumped 5.2% to scale a record high on positive news from its partner Gilead on a rheumatoid arthritis drug.
Meanwhile, Jupiter Fund Management dropped 8.5% as investors booed its plan to consider naming Devon Equity as an adviser for its European Opportunities Trust.
(Reporting by Amy Caren Daniel, Susan Mathew and Sruthi Shankar in Bengaluru, and Helen Reid in London; Editing by Hugh Lawson)
By Susan Mathew and Sruthi Shankar