Across the board, the centre-right European People's Party was set to win 212 out of the 751 seats, with 28.23% across the bloc, according to estimated results issued by the European Parliament. That would make it the biggest group - but with more than 60 seats fewer than before.
That put it ahead of the Socialist group with 186 seats (24.77%), Liberals with 70 (9.32%) and Greens 55 (7.32%).
EPP leader Jean-Claude Juncker insisted the majority of people had voted to be a part of Europe.
"The extreme right, contrary to what some of the media has said, did not win this election," he said.
"We will have a clear pro-European majority in this house," added the man who is the frontrunner to be the next president of the European Commission.
The Eurosceptic Europe of Freedom and Democracy group, incorporating the UK Independence Party (UKIP), appeared to have about the same number of seats as last time.
But the number of non-attached right-wing MEPs is set to rise, boosting the Eurosceptic camp.
UKIP leader Nigel Farage, commenting on his party's success in Britain, said: "The inevitability of European integration ends tonight."
The anti-bailout hard-left group in parliament was set to make big gains, largely thanks to Syriza in Greece and United Left in Spain, gaining about 12 seats.