efe-epaLaura Perez-Cejuela and Laura Zornoza Brussels

The center-right European People’s Party and center-left Progressive Alliance of Socialists and Democrats won the largest share of the votes in Sunday’s European parliamentary elections but have lost their combined majority after a surge for the Greens, the Liberal Democrats and some far-right parties.

Turnout across the European Union was 50.5 percent, the highest in 20 years. Just 42.6 percent turned out in the previous elections in 2014.

Provisional results show that the EPP has won the largest number of seats with 179, or 22 percent of the vote, down from the 221 seats the group won in 2014.

S&D also suffered similar losses compared to four years ago but will remain the second largest in parliament after taking 150 seats (20 percent), while the Alliance of Liberals and Democrats for Europe (ALDE) secured 107, or 14.2 percent, an improvement of 40 seats.

The Greens/European Free Alliance were the fourth largest group with 70 seats (9.3 percent), 15 more than in 2014, thanks to strong results in Finland, Germany, France and Portugal.

The result means that the EPP and S&D will not be able to form a “grand coalition”, having failed to reach the minimum of 376 seats.

The two major parties will need to form alliances with the ALDE or the Greens/EFA to have parliamentary majorities.

The rise of liberal and green parties suggest that the populist and nationalist surge demonstrated in recent national European elections appears to have stalled.

Although they have won in Italy, France and Hungary, right-wing, nationalist leaders did not fare as well as expected.

Instead, pro-EU Green and liberal parties have gained significant ground, although European politics are likely to become even more fragmented in the wake of Sunday's vote.

An exception to that trend is the strong showing from the British Brexit Party, led by prominent eurosceptic and leading campaigner in favor of the UK’s withdrawal from the EU, Nigel Farage.

The newly-formed party gained 28 seats amid huge losses for the British Conservative and Labour Parties.

The far-right Europe of Freedom and Direct Democracy group will increase its representatives in the EP from 48 to 56 seats, a victory for France's Marine Le Pen, along with parties like Italy's Northern League, Austria's FPÖ, the Netherlands' PVV and Belgium's Vlaams Belang.

The European Conservatives and Reformists, of which the Tory party under outgoing prime minister Theresa May are a member, won 58 seats (7.7 percent), a loss of 12.

Elections for the EP, the world's second-largest democratic legislature after India's, were held in the 28 EU countries from Thursday through Sunday.

More than 400 million people were eligible to vote.

A total of 751 members are elected to the European Parliament, which has been directly elected since 1979.

National governments have the final say on all important matters in the EU, but the legislature can influence rules on issues ranging from security to mobile phone-roaming and can strike down the bloc's trade deals or appointees for the bloc's top jobs.

The new balance of power will also need to be reflected in the appointment of several top EU officials, including the president of the European Central Bank. That selection process will begin Tuesday when EU leaders meet in Brussels for a special summit.