199 seats in the Hungarian parliament are up for grabs. That was the highest turnout figure at that time since at least 1998.
Preliminary results are expected to be delayed by the late voting at some stations.
Polling stations were meant to close at 19:00 (17:00 GMT), but some are staying open hours later due to long queues.
Hungary ruling Fidesz party is unlikely to win a two-thirds parliamentary majority, Fidesz's parliamentary group leader Gergely Gulyas told private broadcaster ATV after Sunday's election produced a higher-than-expected turnout.
Hungary's Viktor Orban, a hardliner on immigration in Europe, pledged to fight for his country after casting his vote on Sunday in an election that is expected to give him a third straight term in office.
Hungarian Prime Minister Viktor Orban is seeking a fourth term on a platform that openly demonizes migrants to Europe.
If he wins, as is likely, Mr Orban has promised to cut income tax and pass pro-growth economic policies.
Though Orban has campaigned heavily on anti-migration policies, voters are more concerned with government corruption, poverty, and the country's health care system.
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Long lines of voters were reported also at the Hungarian embassies in London and Paris. "Alongside high voter turnout, the country will have a strong, legitimate parliament".
Analysts say the high turnout, especially in opposition-leaning Budapest and other big cities, may help other parties to overcome a mainly first-past-the-post election system which disadvantages the divided opposition.
'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. "The Hungarian political landscape will dramatically change today".
Orban has far-right admirers across Europe who like his tough line on migrants and a landslide win would show that his single-issue campaign, arguing that migration poses a security threat, had paid off.
Meanwhile Jobbik leader Gabor Vona cast his ballot in the northeastern town of Gyongyos, saying that the result would "determine the fate of Hungary not just for four years but... for two generations".
Uncertainties about Mr Orban's margin of victory are caused by Hungary's electoral system in which voters cast two ballots, one for an individual candidate in their region and another for a party list.
Opposition parties have urged Hungarians to vote tactically for the opposition candidate with the best chance to defeat the Fidesz candidate in the 106 individual districts - but it's not clear how much impact that will have.
Tamas Boros of the Policy Solutions think-tank says the high voter figures mean either "overwhelming support" for Prime Minister Viktor Orban's severe anti-migrant policies or the end of his populist, right-wing Fidesz party's omnipotence.
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