The pan-European STOXX 600 <.STOXX> index had a strong start to the week, gaining 0.5 percent after ending Friday near its lowest close since early April.
The export-oriented DAX <.GDAXI> rose 0.2 percent and Italy's FTSE MIB <.FTMIB> jumped 2.3 percent - its biggest gain in three months.
Anxiety over a new stage in a U.S.-China trade war clouded sentiment.
Late on Friday, Trump warned he was ready to impose tariffs on virtually all Chinese imports, threatening duties on another $267 billion of goods on top of $200 billion worth set for levies in coming days.
"First-round income effects from tariffs on $250 billion of imports are a rounding error for the $19 trillion U.S. economy," wrote JP Morgan analysts.
"But second-round impacts through lower business and consumer confidence and tighter financial conditions are much harder to estimate, in part because no President in living memory has weaponised trade policy like this one has."
Rising trade tensions were eclipsed by comments from Italy's finance minister providing comfort to those fearing a bigger Italian budget deficit.
Italian banks <.FTIT8300> rose as the country's government bonds rallied after Giovanni Tria predicted yields would drop when the government laid out its budget for 2019.
Shares in Intesa Sanpaolo, Banco BPM, and Mediobanca all rose more than 4 percent.
UniCredit gained 4.9 percent after its chairman said the bank, Italy's largest by assets, would assess strategic options as it planned for 2019. He was responding to a question about a possible merger with Societe Generale.
Italian defence company Leonardo jumped 8 percent on the news - after Friday's close - that it would exercise a right of first refusal to buy the 98.5 percent of Vitrociset it didn't already own.
Leonardo thwarted the bid of Fincantieri which in August signed a deal to buy 98.5 percent of Vitrociset in a joint consortium with Mer Mec.
On Sunday, Josef Ackermann, former CEO of German lender Deutsche Bank, said in an interview with Bloomberg TV that Europe needed bank mergers to create a regional champion.
German lenders Commerzbank topped the DAX with a 2.4 percent gain, while Deutsche Bank, which has been rumoured as a possible partner, fell 0.4 percent.
Elsewhere, Richemont rose 1.1 percent after the Cartier maker appointed Jerome Lambert CEO and posted a 10 percent rise in five-month sales.
"His appointment is likely to be welcomed amid some investor concerns about a long-term successor at the group," said Kepler Cheuvreux analyst Jon Cox, affirming a buy rating on the stock.
"The strong sales figure is likely to support a stock that has drifted versus peers and trades at almost a 30 percent discount," he added in a note.
The solid update supported shares in peer Swatch, which gained 0.7 percent.
In the UK, RPC Group jumped 18 percent after Europe's biggest plastics packager said it was in early talks with funds about a takeover offer for the company. It was the biggest gainer on the STOXX.
(Reporting by Danilo Masoni and Helen Reid, editing by Andrew Heavens)
By Danilo Masoni and Helen Reid
