Marches in Germany were held under the banner of "One Europe for Everyone: Your Voice Against Nationalism" in cities including Berlin, Cologne, Leipzig, Frankfurt, Munich and Hamburg.
Organizers from more than 70 groups support the European Union, but also urge changes in migration policy such as support for refugee rescue missions in the Mediterranean Sea.
Other gatherings under the slogan "No to Hate, Yes to Change" were planned in Budapest, Genoa, Utrecht, Warsaw, Bucharest and other cities.
In Bucharest, thousands turned out at Victoria Square, and the crowd formed a heart with the message: "Romania loves Europe."
"We want to tell them that their vote matters and that it's very important to go out and vote, to express their selection and to show Europe that Romania loves Europe," rally organizer Catalina Hoparteanu said.
The dpa news agency said organizers reported 20,000 protesters in Berlin, while police estimated 10,000 in Munich, 14,000 in Frankfurt, and 10,000 in Hamburg.
The 751-seat European Parliament has limited powers but the poll is being seen as a test of strength both by right-wing, populist and nationalist groups who want curbs on immigration and more authority for national governments on the one hand, and on the other by center-left and center-left mainstream parties who support the EU as a bulwark of cooperation among its 28 member states, rule of law and democracy.
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