"This is when all those who want a change of government. ask all those who have yet to vote to by all means go and vote".
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.
"Migration is like rust that slowly but surely would consume Hungary", he said. "I am asking everyone to take part in the election".
A strong win for Orban would boost other right-wing nationalists in Central Europe, in Poland and in neighboring Austria, and expose cracks in the 28-nation EU.
Orban and his wife voted early in the morning at a school in the leafy Zugliget suburb of Budapest. "The EU is in Berlin, in Budapest, in Prague and in Bucharest".
He has campaigned heavily on his unyielding anti-migration policies, although voters say they are more concerned with poverty, government corruption and the country's underfunded health care system.
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.
Polls predicted the triumph of Orban's Fidesz party and its allied Christian Democratic People's Party (KDNP).
According to a poll by Zavech research institute published on Friday, Fidesz had 46 percent support among decided voters, while former far-right Jobbik, which has reshaped its image into a more moderate force, had 19 percent.
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Mr Vona said the question is not about migration but the large number of Hungarians leaving the country and heading to western Europe in search of higher wages and better prospects.
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".
The anti-immigrant campaign has gone down well with numerous roughly two million core voters of Fidesz.
However, the polls could be unreliable as one-third of voters are undecided and many hide their voting preference.
In March the government also gave pre-election handouts to millions of families and pensioners. The Socialists came in third with 14 percent.
"Voter turnout is at record high", tweeted Tamas Boros, co-director of the Policy Solutions think tank.
In last elections of 2014, Orban's coalition Fidesz-KDNP won 133 seats, securing two thirds of the parliament, also known as a super majority.
If borne out, Mr Orban will likely seize on the results as vindication of his clashes with European Union institutions over his hardline anti-immigration policies and rejection of the EU's refugee resettlement programme, as well as his moves to clamp down on civil society groups. Businessmen close to Fidesz have acquired stakes in major industries like banking, energy, construction, and tourism, profiting from European Union funds.