European governments fear a good showing for euroskeptics in the vote, which begins on Thursday, May 23, and runs to Sunday, May 26, will disrupt Brussels decision-making.
Opinion polls predict a significant advance for nationalist and populist forces opposed to closer European Union integration and threatening mainstream reform efforts.
French President Emmanuel Macron called the vote the most important European parliamentary election since the first in 1979 and warned the EU faces "an existential threat."
Turnout has fallen in each EU vote since 1979, and mainstream leaders hope Britain's Brexit spectacle and a scandal for the Austrian far-right will mobilize voters.
'Stand as one'
The outgoing president of the European Commission, Jean-Claude Juncker, urged an audience at a trade union convention in Vienna "to fight where it is worth fighting."
"And it is worth making it clear for the next decades – also in the coming European elections – that trade unionists, social democrats and Christian democrats, others should stand there like one man when it comes to pushing back the danger from the extreme right," he said.
British voters – along with the Dutch – will vote first on Thursday, with those in the 26 other member states following suit over the next 3 days.
In Britain, Nigel Farage's anti-EU Brexit Party is expected to top the polls, and euroskeptic populists are riding high in Italy and breaking through elsewhere.
The euroskeptics have not had it all their own way, though.
In Austria, far-right Vice-Chancellor Heinz-Christian Strache was entrapped on hidden-camera footage offering to sell influence to a supposed representative of a Russian oligarch.
'Filling their pockets'
Strache resigned, but the scandal has undermined the attempt by Austria's conservative Chancellor Sebastian Kurz to draw the extreme right into a coalition government.
"What happens there certainly has not only a national, but a pan-European meaning," Germany's minister for European affairs Michael Roth said in Brussels.
"It becomes clear that the strategy has failed to contain, to immobilize, to disenchant nationalists and populists through governmental responsibility," he said.
Roth said far-right figures have "also filled their pockets" in other EU countries and accused them of paying "lip service" to democracy and the rule of law.
Accusations from the center will not deter the populists, who hope to mirror the national success of Italian vice premier Matteo Salvini and Hungary's Viktor Orban.
"Everything has changed," French far-right leader Marine Le Pen told Agence France-Presse, ahead of a vote in which she hopes to beat Macron's new Renaissance movement into second place.
"Before we were on our own on the European scene... But in the space of a few months, a whole range of political forces have risen up in spectacular fashion."
The run-up to the vote has seen political tensions mount.
In Germany, the far-right AfD party cancelled its election night party in Berlin, citing alleged "threats from left-wing terrorists."
And in Britain on Monday, May 20, Farage had to abandon a walkabout in the city of Newcastle after a protester doused him with milkshake.
Opinion polls at the start of the campaign pointed to around 173 members being elected to the 751-member Strasbourg assembly from far-right populist, euroskeptic or nationalist groups.
Meanwhile, the main center-right and center-left groupings that have dominated pan-European politics in recent years look set to lose ground.
According to opinion polls, the top two groups could lose 30 seats each, meaning they will not be able to form a majority and may have to reach out to liberals and Greens.
The liberal ALDE hopes for an infusion of new blood from Macron's Renaissance and from the Spanish party Ciudanos.
For Brussels insiders, the big night will not be Sunday when the first results of the parliamentary race emerge, but two days later when the national leaders meet for dinner. – Rappler.com