BRUSSELS (Reuters) - Voting began in the Netherlands on Thursday at the start of a four-day election across the European Union to a new European Parliament that will face mounting security, industrial and political challenges.

Voting to the EU legislature will be held in Ireland and the Czech Republic on Friday, Malta, Slovakia and Latvia on Saturday, and in the rest of the 27 EU countries on Sunday.

The Dutch vote encapsulates the EU's main internal political challenge - the rising popularity of euro-sceptic and nationalist far-right parties that want to dismantle the EU for within.

External challenges facing the EU included industrial competition from China and the United States, a security threat from Russia and the existential threat of climate change.

Opinion polls showed the Dutch anti-immigration Freedom Party (PVV) of nationalist Geert Wilders was set to make gains, tying with the Labour/GreenLeft combination. Both were projected to win eight seats in the European Parliament.

Wilders failed to secure a seat in the previous European election in 2019 and although the polls show Europe's centre-right is likely to win the most seats in the new EU legislature, far-right parties are expected to make gains.

The 720-seat parliament co-decides with national governments on laws that govern the bloc's single market of 450 million people, its 1-trillion-euro ($1.09 trillion) long-term budget, fiscal rules and laws to prevent climate change.

First projections of results are expected after 2100 GMT on Sunday, following exit polls soon after 1800 GMT.

European Greens, facing a farmer and industry backlash against costly EU policies limiting CO2 emissions, look set to be among the big losers.

Polls show pro-European parties on the centre-right and centre-left, liberals and Greens will have a smaller majority than in the outgoing parliament, complicating efforts to push through new EU laws or increase EU integration.

FIVE-YEAR TERM

The new parliament's term will end in 2029. It will decide on the EU's next seven-year budget, which must be in place from 2028, with Ukraine, Moldova and countries of the Western Balkans seeking membership.

If those countries are to accede, EU governments and the parliament will need to agree on internal changes to how the bloc operates, including its agriculture subsidies and funds to even up living standards across the EU.

The rule of unanimity in voting may also need changing to meet the requirements of a larger bloc.

The composition of the new parliament will also be the starting point for the choice of the new head of the European Union executive body, the European Commission, which has the sole right to propose new EU laws.

Polls show Europe's centre-right is likely to win the most seats in parliament. This puts their candidate, current European Commission President Ursula von der Leyen of Germany, in pole position to be appointed for a second term.

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(Reporting by Jan Strupczewski, Editing by Timothy Heritage)

By Jan Strupczewski