Right-wing nationalist parties look set to surge in elections across Europe this week, but the shock wave will travel slowly due to rifts among the political forces.

Many of the parties see former President Donald Trump as a model . They pledge to peel back Brussels’ power and shift European Union policy on hot-button issues including migration and climate policies .

Balazs Orban , political director for Hungary’s nationalist Prime Minister Viktor Orban , believes the EU elections put a long-elusive goal within reach: building a single nationalist alliance to reshape the bloc.

Across Europe, opposition to the EU’s expanding powers is increasing, he said. A strong right-wing result this week, buttressed with a potential Trump victory in November, could force EU leaders to abandon their search for an ever more centralized bloc, believes Orban, who is no relation to the prime minister.

“I think in the short term, the entire political environment can change,” he said.

The initiative is hitting setbacks.

Italy’s Prime Minister Giorgia Meloni gestures, as she visits the construction site of the migrant processing centre in Shengjin, Albania June 5, 2024. REUTERS/Florion Goga

Relatively moderate right-wing leaders, including Italian Prime Minister Giorgia Meloni , are noncommittal and eager to explore ties with center-right politicians.

France’s more hard-line National Rally, meanwhile, broke ties last month with its EU partner, the Alternative for Germany, after spying allegations and other scandals at the AfD .

Jan Zahradil , an EU lawmaker and former president of the European Conservatives and Reformists, one of the bloc’s two right-wing political groups, said this week’s vote could change the political atmosphere. But he believes it will take many nationalist victories in member state elections over coming years to build a new force that could reshape Brussels.

“It will be a process. It won’t be a revolution,” Zahradil said.

The nationalist right-wing agenda faces two significant hurdles in Europe because the EU is a grouping of 27 sovereign states, not one federal state like the U.S. To reach decisions on most big issues, governments must compromise. Adding complexity, leaders win a seat at the EU table through their national elections—not EU-wide elections—and domestic political pressures make it hard to forge a pan-EU agenda.

epa11317716 A man wearing a suit of EU flag attends the open days of European institutions on ‘Europe Day’ in Brussels, Belgium, 04 May 2024. Thousands of visitors attended the Europe Day, an annual celebration of peace and unity in Europe, that falls this year a month ahead to the European elections to renew members of the European Parliament EPA/FREDERIC SIERAKOWSKI

Up to 370 million EU voters go to the polls from Thursday through Sunday to pick lawmakers for the European Parliament, a body whose main power lies in amending or blocking EU initiatives. It must also approve the EU’s next leadership team.

Turnout is usually modest but the elections offer a twice-a-decade barometer of Europe’s political mood. Some recent polls suggested nationalist parties could win close to 200 of the parliament’s 720 seats, a 50% rise on the 2019 result.

Right-wing politicians say they have much common ground. They want to tighten restrictions on asylum seekers and reverse climate rules like the 2035 ban on sales of new carbon dioxide-emitting vehicles. They seek to restore national powers over social issues that they contend liberal officials in Brussels seek to advance, such as LGBTQ rights. And they don’t want EU officials doing what they did to Hungary: withholding billions of euros in EU funds because the bloc’s executive body alleges Budapest was breaching rules.

The parties oppose what they argue is a dangerous expansion of Brussels’ political muscle but that EU supporters see as a pragmatic response to recent crises. Pro-EU politicians argue there is a fallacy at the heart of the nationalist critique of Brussels: Almost everything that happens there has the backing of at least a clear majority of the bloc’s elected governments.

The EU in recent years has played a central role in supporting Ukraine and sanctioning Russia. The EU approved an ambitious Green Deal and issued large-scale EU common debt for the first time to raise funds that Brussels controls.

The rise of right-wing nationalists has already shifted the center on some issues, especially migration. When Orban during Europe’s 2015 migration crisis pushed back asylum seekers and built a border fence, it was widely attacked. Now, other governments have followed suit.

Many nationalist leaders are charismatic political veterans.

Dutch nationalist Geert Wilders , who has been under security protection for two decades for his anti-Muslim rhetoric, stunned pundits in November when his party shot to first place in parliamentary elections. Wilders will be the power broker behind a right-wing coalition expected to take office soon, which wants to opt-out from EU rules on accepting asylum seekers and forcibly deport people who lack a residence permit.

Orban, Hungary’s longtime leader and a harsh EU critic, promises a Brussels overhaul. Orban is a big fan of Trump and the feeling is mutual: Trump hailed him as “a smart guy and tough” this week, noting his antimigration stance.

In France, Marine Le Pen has ditched her pledges to leave the EU and softened her National Rally party’s image . But she wants to scrap the Green Deal and further strip migrants’ social benefits. Her party says it could restore policing of national borders within the travel-free Schengen zone to prevent asylum seekers moving across the EU.

Yet on many of the biggest issues facing the EU, right-wing nationalists disagree.

Dutch far-right leader Geert Wilders speaks to the media on the day he campaigns for the EU elections, visiting a market in The Hague, Netherlands June 5, 2024. REUTERS/Piroschka van de Wouw

Orban, Wilders and Germany’s AfD lambasted European sanctions on Russia and the sending of arms and money to Kyiv. Le Pen and Meloni stand with Ukraine. Wilders, forced to compromise in coalition talks, now pledges Dutch support for Kyiv.

Meloni advocates Ukraine joining the EU. Orban and Le Pen reject it.

The parties have zigzagged on whether to hold votes on leaving the EU or the euro. The AfD has said it would hold a referendum if the EU doesn’t change radically. Wilders campaigned on a referendum promise but later ditched it.

Even on immigration, rifts have emerged. Meloni shaped a recent EU compromise easing the rejection of asylum seekers. Orban wants to tear that plan up and adopt a stricter one.

Le Pen recently floated a formal alliance of right-wing parties aimed primarily at wooing Meloni, who won power in 2022 on a strong antimigration platform but has repositioned herself as a mainstream conservative, playing down her far-right roots. She didn’t get a response.

Meloni has won plaudits for helping shape the EU’s agenda, weakening the influence of her Lega Nord junior coalition partner, a onetime separatist party that has turned nationalist and anti-EU under Matteo Salvini , who once donned T-shirts with Russian President Vladimir Putin ’s image.

Jörg Meuthen , a longtime leader of the AfD who has since quit the party, worked in 2019 on a previous effort to unite the right. The clash of views over the agenda and its ultimate failure highlighted nationalist splits.

“There was definitely no common agenda,” he said. “And I’m quite sure that it will not exist in future.”

Thibaut François , a French lawmaker and the National Rally’s spokesman on European affairs, said that even if a fusion of nationalist parties proves impossible, the right can form ad hoc coalitions on priorities. He said disagreements over foreign policy issues, like Ukraine, won’t impede that.

“We are very happy to disagree on these topics because we do think that they are sovereign, national decisions,” François said.

After years of supporting a referendum on France’s EU membership, Le Pen’s party has now recognized that the French people are “very much attached” to the EU structure, he said. But he believes the party is winning the argument that the EU should return to its original shape: a union of nation-states with limited central powers.

The political paths taken by National Rally and Germany’s AfD show how domestic political forces divide Europe’s nationalist right.

Marine Le Pen, President of the French far-right National Rally (Rassemblement National – RN) party parliamentary group, and Jordan Bardella, President of the French far-right National Rally (Rassemblement National – RN) party and head of the RN list for the European elections, attend a political rally during the party’s campaign for the EU elections, in Paris, France, June 2, 2024. REUTERS/Christian Hartmann

Le Pen has tacked toward France’s political center-right to win broader support. An IFOP poll in February suggested Le Pen would win at least 50% in a presidential face-off against her most likely opponents in 2027 if she runs. She received 41% in 2022. She has sought to distance the party from its past antisemitic and anti-Muslim stance and is pushing a new generation of slicker, young politicians.

In Germany, mainstream parties shunned the AfD, which veered sharply right to win over disaffected voters. Meuthen quit in 2022, slamming the party’s “totalitarian overtones.”

German media recently reported that AfD officials attended a meeting that discussed mass deportation of non-ethnic Germans. A German court said the party is officially suspected of extremism, and an aide to the AfD’s top EU elections candidate, Maximilian Krah, was arrested on spying allegations . Krah sparked outrage last month by saying former members of the Nazi SS paramilitary force weren’t automatically criminals. Hours later, the pan-EU Identity and Democracy political bloc—which includes France’s National Rally—ejected the AfD.

Maximilian Krah, member of the European Parliament for the far-right Alternative for Germany and AfD’s top candidate in June’s election to the assembly, gives a statement, after an aide has been arrested in Germany on suspicion of “especially severe” espionage for China, in Berlin, Germany, April 24, 2024. REUTERS/Fabrizio Bensch TPX IMAGES OF THE DAY

Write to Laurence Norman at laurence.norman@wsj.com