Far-right and Eurosceptic parties have made sweeping gains in European Parliament elections, triggering what one prime minister called a political "earthquake" by those seeking to slash the EU's powers or abolish it altogether.

Voters in 21 of the European Union's 28 nations went to the polls yesterday to choose MEPs for the bloc's 751-seat legislature. The other seven countries had already voted in a sprawling exercise of democracy that began on Thursday in Britain and the Netherlands.

One of the most significant winners was France's far-right National Front party, which was the country's outright winner with 26% support- or 4.1 million votes.

"The sovereign people have spoken ... acclaiming they want to take back the reins of their destiny," party leader Marine Le Pen said. She called the results "the first step in a long march to liberty".

French prime minister Manuel Valls, in an impassioned televised speech, called the National Front win "more than a news alert ... it is a shock, an earthquake."

President Francois Hollande's office said he would hold urgent talks today with top government ministers in what French media called a crisis meeting.

All of Europe would have to deal with the fallout, analysts and politicians said.

Pro-European parties "have to take very seriously what is behind the vote", said Martin Schulz of the parliament's Socialist group.

Guy Verhofstadt, leader of the Liberal caucus, conceded as much but said even after the vote, two-thirds of the MEPs would be "people who are in favour of the European Union".

Despite the Eurosceptic gains, established pro-EU parties were forecast to remain the biggest groups in the parliament. The conservative caucus, known as EPP, was forecast to win 211 seats, down from 274, but enough to remain the parliament's biggest group.

The National Front was not the only party benefiting from widespread disillusionment with the EU. Nigel Farage, leader of the Eurosceptic Ukip party, believed he was on track for a historic victory.

"It does look to me (like) UKIP is going to win this election and yes, that will be an earthquake, because never before in the history of British politics has a party that is seen to be an insurgent party ever topped the polls in a national election," he said.

"I don't just want Britain to leave the European Union, I want Europe to leave the European Union."

The first official results had UkipP at about 30%, some 12% higher than the last European elections in 2009.

In Denmark, with 95% of votes counted, the main government party, the Social Democrats, retained their five seats to remain the biggest party.

But the big winner in the elections was the populist, opposition Danish People's Party, which won three more seats for a total of four. A year-old party in Germany that wants that country to stop using the euro single currency reportedly won 6.7% of the vote.

In Greece, with a quarter of the votes counted, the leftist Eurosceptic Syriza party led with 26.49%. The extreme right Golden Dawn party was third with 9.33%.

Doru Frantescu, policy director of VoteWatch Europe, an independent Brussels-based organisation, said Europe's mainstream political parties won enough seats to still muster a majority on issues where they concur.

"The problem comes when the left, the Socialists and EPP will not agree on issues," he said.

In the incoming European Parliament, he said, fringe parties will be able to exert more pressure on key topics, ranging from how liberal to make the internal European market for services or the proper mix of energy sources to which clauses should be scrapped in a proposed trade and investment agreement with the US.

In the Netherlands however, the right-wing Eurosceptic Party for Freedom surprisingly dropped a seat from five to four. Its outspoken leader, Geert Wilders, said his party looked forward to working with Ms Le Pen in Europe, calling her "the next French president".

In Italy, early projections indicated that the main government party, the Democrats led by premier Matteo Renzi, had beaten a challenge by the anti-euro 5-Star Movement of comic Beppe Grillo. The centre-left Democrats were forecast to win 40%, while Mr Grillo's anti-establishment movement would garner 22.5%.

Despite the gains, unity may be hard to find in the fractured Eurosceptic camp.

Ms Le Pen has said she will work with Mr Wilders' party but Mr Farage has ruled out co-operating with either, which have strident 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 favour of the EU despite its rejection of the common currency.

Mr Grillo has said in the past his movement would not ally itself with Ms Le Pen's party, claiming the 5-Stars had a different "DNA".

Conservative caucus leader Joseph Daul put a brave face on the results. "One thing remains certain: EPP is the responsible political force in Europe, which keeps Europe open," he said.

The European Parliament estimated turnout was narrowly up from the last election in 2009, at 43.1%, reversing years of declining turnouts.

Voters also put new parties in the European Parliament, with preliminary results showing that Sweden elected the first MEP from a feminist party and the Dutch returned one representative for the Party for the Animals.

"You know that we have created history don't you? We inspire the world. This is the force of love!" the Feminist Initiative's main candidate, Soraya Post, proclaimed to cheering supporters in Stockholm.