A young woman queuing up to vote in Budapest said she is hoping for a breath of change after the election, but did not reveal who she was voting for.
Mr Orban claims the opposition - collaborating with the United Nations, the European Union and wealthy philanthropist George Soros - wants to turn Hungary into an "immigrant country", threatening its security and Christian identity.
The National Election Office will stop tracking voter turnout at exactly 6.30pm local time.
High turnout has forced some Hungarian polling places to remain open, delaying the announcement of results in the national election. In 2014, the participation rate at the end of the day was 61.24 percent.
Experts say the large turnout in Hungary's parliamentary election could "dramatically change" the country's politics. "The Hungarian political landscape will dramatically change today".
Voters were no longer allowed to join queues at polling stations from 1700 GMT, but those already in line were being allowed to cast their ballots, meaning voting could continue for hours more at the busiest stations. The opposition Socialist Party urged authorities to "at least distribute water" in districts where voters were waiting in line, sometimes for hours.
Some 8.3 million Hungarians are eligible to vote, with preliminary results expected Sunday night. Despite being tipped to take two-thirds of the 199 parliamentary seats for a third time only months ago, ruling party officials have said that now appears out of reach.
"Today will decide whether Hungary becomes an emigrant country or not - and I wouldn't like Hungary to be an emigrant country", Mr Vona said.
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Gabor Vona of the nationalist Jobbik party urged his supporters not to become complacent.
Gergely Karacsony, the leading left-wing candidate for prime minster, said Sunday the high turnout was good news for those in favor of preventing Prime Minister Viktor Orban from winning his third consecutive term.
Uncertainties about Orban's margin of victory are caused by Hungary's complex electoral system in which voters cast two ballots, one for an individual candidate in their region and another for a party list.
Hungarian Prime Minister Viktor Orban has cast his vote in the parliamentary election, saying the ballot is about "Hungary's future".
Orban and his wife voted early in the morning at a school in the leafy Zugliget suburb of Budapest.
Orban, who focused his campaign on his harsh anti-migration stance, says it's a "misunderstanding" that his frequently harsh criticism of Brussels was directed at the whole of the European Union.
Although Orban's actions, including refusing to participate in the EU's refugee resettlement scheme, have sometimes annoyed other European governments, Fidesz is afforded a measure of protection by virtue of its membership of the main centre-right EPP grouping in the European Parliament. The EU is in Berlin, in Budapest, in Warsaw, in Prague and in Bucharest.
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