Hungarians are heading to the ballot boxes to vote in a landmark parliamentary election that could oust Viktor Orbán after 16 years in power and potentially reshape the central European country’s relations with the EU, Moscow and Washington.

During the campaign, Orbán – the EU’s longest-serving leader – has trailed in the polls as he faces an unprecedented challenge from Péter Magyar, a former elite member of Orbán’s Fidesz party.

The challenge to Orbán’s power has sent rightwing leaders from around the globe scrambling to rally behind him. This week, JD Vance turned up in Budapest for a two-day visit, the US vice-president telling reporters that his aim was to help Orbán win.

Donald Trump has also repeatedly endorsed Orbán, most recently on Friday when he vowed on social media that he would bring US “economic might” to the country if Orbán was re-elected. Months earlier, leaders including Italy’s Giorgia Meloni and Israel’s Benjamin Netanyahu made it clear that they were backing Orbán.

The result is an election that has played out on the global and domestic stages, as Orbán has argued the country’s biggest threat is the war in Ukraine and he alone is capable of keeping the peace, while Magyar has focused on domestic issues with pledges to crack down on corruption, repair the strained relationship with the EU and funnel funds into the country’s crumbling public services.

By midday on Sunday, turnout had climbed to a record 37.98%, according to the country’s national election office, meaning about 876,000 more voters had cast their ballots compared with the 2022 elections.

The two leading candidates voted at separate polling stations in Budapest early on Sunday, with Magyar, 45, telling reporters that Hungarians were writing history as they chose between “east or west, propaganda or honest public discourse, corruption or clean public life”.

Orbán, 62, who has swept the last four elections, said the country needed to stay united in order to resist “approaching crises”. He told reporters he had come to win.

After Magyar and his centre-right Tisza party crisscrossed the country, holding as many as six rallies a day, most polls put his party in the lead. Analysts expressed caution, however, as undecided voters and Hungarians abroad could still sway the result, as could alleged vote buying.

For many in Hungary, Sunday’s vote will be a test of how deeply Orbán’s political system is embedded, after the rightwing populist leader spent more than a decade working to transform Hungary into a “petri dish for illiberalism”, rewriting election laws to his party’s benefit, manoeuvring to put loyalists in control of an estimated 80% of the country’s media and clamping down on dissenting voices.

The result will be closely watched by the Maga movement and the global far right, many of whom have long cited Orbán as an inspiration and sought to follow his playbook.

Questions have swirled over Orbán’s government and its relationship with Moscow amid allegations of Russian interference in the election, as well as audio that appeared to suggest a minister had shared confidential EU information with the Russian government.

Orbán’s government has cited the leaks – including a transcript in which Orbán reportedly told Vladimir Putin “I am at your service” – as evidence of foreign interference.

Analysts have pointed to three possible outcomes of the election: a Magyar majority that Orbán accepts; a Magyar majority that Orbán does not accept; or an Orbán majority.

If Magyar wins, many will be watching to see whether he gains a simple majority or a super-majority – a win of least two-thirds of the 199 seats in Hungary’s parliament. A super-majority would allow Magyar and his party to amend the constitution and laws, allowing them to reverse some of the changes made by Orbán and Fidesz and potentially unlock EU funds.

In the lead-up to the election, most polls had pointed to a big win for Magyar and his Tisza party, said Zoltán Kész, a former member of Fidesz. “If we were talking about a normal democracy, I would say they could have a super-majority in parliament because of the polls that we’re seeing,” he said. “But this is not a normal democracy.”

Fidesz’s transformation of Hungary’s electoral system and gerrymandering of its 106 voting districts will require Tisza to gain an estimated 5% more votes than Orbán’s party to achieve even a simple majority.

At a Friday night rally for Orbán in Székesfehérvár, a city of about 100,000 people in central Hungary, hundreds of people turned up, eagerly waving flags and cheering, as cameras panned over the city where the first kings of Hungary were crowned and buried.

“I’m so happy to be here,” gushed Cecília, 78. “He’s the best leader in the world.” Sunday was set to be the fifth time since 2010 she had voted for Orbán. “Viktor Orbán will win, of course, with a super-majority,” she said.

Others were more circumspect. Sándor, 69, said: “When it comes to polls, it depends on who does them, but the situation does seem tense. I’m worried for him [Orbán]. He seems tired.”

Scattered among the crowd were also a handful of Magyar supporters. “I was curious to hear the prime minister speak,” said Richárd, 27. What he had heard, he said, hinted at a fundamental difference between the two leading parties. “For 16 years, Fidesz has been campaigning on hatred and fear,” he said. “While Tisza has been trying to express hope at all of their events.”