According to preliminary results with 85 percent of votes counted, National Election Office data projected Fidesz to win 133 seats, a two-thirds majority in the 199-seat parliament. Opposition parties are keen to make sure Mr Orban's bloc does not sweep to a super-majority in which the autocratic leader could easily push through constitutional changes.
The government also points to Hungary's solid economic growth, which has brought steadily rising wages, and says this would be at risk in the event of an opposition victory.
Speaking at a recent campaign rally, Orban accused the European Union of "trying to take away our country". Such an outcome would allow Orbán to pursue radical change, perhaps tightening his grip Hungary in the same vein as Poland.
Orban is seeking his fourth term.
'We are celebrating democracy and it seems like this feast will be lovely because many of us are taking part, ' said Gergely Karacsony, the leading candidate of the left-wing Socialist and Dialogue parties.
Though Orban has campaigned heavily on anti-migration policies, voters are more concerned with government corruption, poverty, and the country's health care system.
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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Two victims suffered gunshot wounds and were transported to a local hospital with non-life threatening injuries. Authorities were already on the scene and the situation was still developing, police reported in the message.
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Turnout will be a key factor in determining the result, with higher participation thought to benefit the opposition.
After casting his vote in a wealthy district of Budapest with his wife, Orban said Hungary's future was at stake in the vote.
Vona's Jobbik party started out as xenophobic group well known for its anti-Semitic views. He refused to take part in the EU's refugee resettlement programme and he has praised Russian leader Vladimir Putin.
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.
A high turnout in a 2002 vote consigned Orban to eight years of opposition. He claims the European Union, the U.N., Hungarian-American financier George Soros and the civic groups he sponsors are all conspiring to force Hungary to take in thousands of mainly Muslim migrants to weaken its independence and its Christian identity and culture.
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 leaders reject Orban's claims that they are controlled by Soros and support mass immigration. The EU is now in Berlin, in Budapest, in Warsaw, in Prague and at Bucharest.