BRUSSELS — Exit polls showed the far right and Euroskeptics making sweeping gains in European Parliament elections Sunday, signaling a major political shift toward parties that want to slash the European Union’s powers or abolish it altogether.

Polls in recent days had predicted Euroskeptics could snag as many as a third of the seats in the EU’s 751-seat legislature in the vote ending Sunday.

One of the most significant winners appeared to be France’s far-right National Front. Two polling companies said the party, led by Marine Le Pen, was outright winner in France with one-quarter of the popular vote.

In Greece, neo-Nazi party Golden Dawn also appeared to make gains, taking some 9 percent of the vote according to exit polls.

Voters in 21 of the European Union’s 28 nations voted Sunday. The other seven countries had already voted, in a sprawling exercise of democracy that began Thursday in Britain and the Netherlands.

The results — official returns were expected later Sunday — will help determine the bloc’s future leaders and course. They could herald changes in EU policy in areas ranging from border control and immigration to a new trade and investment agreement being negotiated with the US.

The National Front was not the only party benefiting from widespread disillusionment with the EU.

Unofficial exit polls reported a surge in support for Britain’s UKIP party.

Pollsters said the Danish People’s Party was also on target to become Denmark’s biggest party with 23 percent of the vote, and a year-old party in Germany that wants that country to stop using the euro single currency reportedly won 6.7 percent of the vote.

Reacting to her party’s strong showing, Le Pen said Sunday, “This hope should unite us.”

In the Netherlands, however, the right-wing Euroskeptic Party for Freedom surprisingly dropped from second to fourth place, pollsters reported.

Even in victory, unity may be hard to find in the fractured Euroskeptic camp.

Le Pen has said she will work in the Parliament with the Dutch Party for Freedom, but UKIP leader Nigel Farage has ruled out cooperating with both those parties, which have stridently anti-immigrant platforms.

“We won’t work with right-wing populists,” Alternative for Germany’s leader Bernd Lucke also said after the vote, insisting his party was generally in favor of the European Union despite its rejection of the common currency.

The European Parliament estimated turnout as almost identical to the last election in 2009, at 43.1 percent.