After seat gains, how would far-right seek influence on EU policy?
The new parliament's first test, to determine the next Commission president, could come as early as July.
Europe's nationalist parties capitalised in the European Parliament election on voter disquiet over spiralling prices, migration and the cost of the green transition and will now seek to translate their seat gains into influence on EU policy.
Nationalist, populist and eurosceptic parties were on course to win just under a quarter of seats in the EU assembly, according to the chamber's own projections.
It reflects a growing trend in the West to turn from the mainstream and status quo towards radical alternatives such as former and possibly future US President Donald Trump.
In previous elections, radical right parties talked of leaving the European Union or its single currency, echoing the calls of British Brexiteers. Now these parties want to influence it from within.
Nationalist prime ministers are already in place in Hungary, Italy and Slovakia, right-wing parties are governing or supporting in Finland and Sweden, while Geert Wilders' anti-immigrant Freedom Party appears poised to enter a ruling coalition in the Netherlands.
Armida van Rij, senior research fellow at Chatham House, said "cordon sanitaire" policies to exclude hard right parties are eroding.
"People know now it's not just a lost vote," she said, adding that populist parties' extensive use of social media is also bringing in younger voters.
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Gerolf Annemans, a lawmaker of Belgium's Vlaams Belang party, said the new parliament should scrap a recently agreed EU migration pact, soften the Green Deal and find a more right-leaning alternative to European Commission President Ursula von der Leyen.
The new parliament's first test, to determine the next Commission president, could come as early as July. Von der Leyen will be in pole position for a second term given her centre-right European People's Party (EPP) is set to be the biggest group.
However, she may need support from some right-wing nationalists, such as Italian Prime Minister Giorgia Meloni's Brothers of Italy, to secure a parliamentary majority, giving Meloni and allies more leverage.
Luigi Scazzieri, senior research fellow at the Centre for European Reform, said the centre-right EPP has already cooled on attempts to fold broader environmental policies into the Green Deal package. Scazzieri said he could also envisage a right-wing push to increase external processing of migrants and a tougher passage of reforms required to allow EU enlargement, such as reducing the need for unanimity in decisions.
"I expect this to play out over time rather than have an immediate effect," Scazzieri said. "They also have quite a powerful shaping effect on the broader political debate."
Corina Stratulat, associate director of think tank the European Policy Centre (EPC), said a key determinant would be the degree to which the radical right could unite. They do not have a strong record.
French far-right leader Marine Le Pen has urged Italy's Meloni to form a right-wing grand alliance, but Le Pen's party and allies expelled Alternative for Germany only last month, while an alliance including Hungarian Prime Minister Viktor Orban's Fidesz would be a step too far for some of Meloni's allies, such as Belgium's N-VA.
An EPC study concluded that this lack of cohesion means the radical right would need to win more than 70 percent of European Parliament seats to completely control vote outcomes - a figure they almost certainly will not reach.