Frankfurt's DAX 30 index jumped 0.8 percent to 12,110.65 points, while the Paris CAC 40 gained 0.7 percent to 5,356.50 compared with closing levels on Friday.

Eurosceptic and populist parties failed to make significant gains in Germany in the European Parliament elections, according to results released on Sunday.

Marine Le Pen's far-right National Rally finished top in France, but pro-EU President Emmanuel Macron's centrist alliance was close behind.

"The catastrophe that some people predicted for Macron has not taken place and the RN has a significant score, but not a spectacular one," analyst Zaki Laidi from the Cevipof political institute said.

Oanda analyst Alfonso Esparza said that the "European parliament results did not provide major surprises but a continuation of political trends".

Trump meanwhile spurred investor optimism by saying there was a "very good" chance of a deal with China as the world's top two economies clash over their trade relationship.

"I think sometime in the future, China and the US will have a great trade deal and we look forward to that," Trump said after talks in Tokyo with Japanese Prime Minister Shinzo Abe.

The US and UK markets were closed on Monday.