BRUSSELS -- Across Europe, anti-EU populists and proponents of closer unity made a final push for support Sunday as 21 nations went to the polls in a continent-wide battle for influence at the European Parliament.

Right-wing nationalists who want to slash immigration into Europe and return power to national governments are expected to make gains, though mainstream parties are tipped to hold onto power in the 751-seat legislature that sits in both Brussels and Strasbourg.

The election began on Thursday, but most of the EU's 28 member states, including the biggest of all, Germany and France, are voting on Sunday, and the results are expected overnight. Some 426 million people are eligible to vote.

"I don't want to see a right-populist Europe (that) wants to destroy the idea of togetherness," said Manfred Weber, the lead candidate of the Christian Democrat centre-right EPP group, currently the biggest in the legislature.

Leading the challenge to the established order is Italy's hard-line interior minister, Matteo Salvini, head of the League party, who is assembling a group of like-minded parties from across Europe.

"We need to do everything that is right to free this country, this continent, from the illegal occupation organized by Brussels," Salvini told a rally in Milan last weekend that was attended by the leaders of 11 nationalist parties.

As he voted in Budapest on Sunday, Hungarian Prime Minister Viktor Orban said he hopes the election will bring a shift toward political parties that want to stop migration.

The migration issue "will reorganize the political spectrum in the European Union," said Orban, who recently met with Salvini but has not yet committed to joining the Italian's group.

In the face of a more united hard-line right wing in the parliament, traditional parties like the EPP and the centre-left socialist S&D group want the mainstream to build a strong coalition to stave off the fringe parties.

Spanish caretaker Prime Minister Pedro Sanchez called on "all the political forces to open a horizon of political stability."

Projections released by the European Parliament last month show the EPP bloc losing 37 of its 217 seats and the S&D group dropping from 186 seats to 149. On the far right flank, the Europe of Nations and Freedom group is predicted to increase its bloc from 37 to 62 seats.

Proponents of stronger EU integration, led by French President Emmanuel Macron , argue that issues like climate change and reining in immigration are simply too big for any one country to tackle alone.

Macron, whose country has been rocked in recent months by the populist yellow vest movement, has called the elections "the most important since 1979 because the (European) Union is facing an existential risk" from nationalists seeking to divide the bloc.

In Austria, Chancellor Sebastian Kurz said Sunday that he hopes the elections will strengthen the centre rather than parties on the far right and left.

Austria is one of the countries where the vote also has importance to national politics, serving as a first test of support ahead of a national election in September following the collapse of Kurz's governing coalition a week ago.

In Belgium, a general election is taking place alongside the European vote, while Lithuanians will vote in the second round of their presidential election.

Britain is taking part in the vote even though it is planning to leave the bloc, after the government missed its March 29 deadline to approve divorce terms. Its EU lawmakers would lose their jobs as soon as Brexit happens.

Sunday promises to be a long day and night for election watchers -- the last polls close at 11 p.m. (2100 GMT) in Italy but the European Parliament plans to begin issuing estimates and projections hours earlier with the first official projection of the makeup of the new parliament at 11:15 p.m. (2115 GMT).

As the dust settles on four days of elections, European leaders will begin the task of selecting candidates for the top jobs in the EU's headquarters in Brussels. The leaders meet for a summit over dinner Tuesday night.

Current European lawmakers' terms end July 1 and the new parliament will take their seats in Strasbourg the following day.