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.
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.
But others disagreed, such as kindergarten nurse Szilvia Nagy in the northeastern town of Gyoengyoes, who said: "I would like to change the government, because I desire a nicer future".
It is known that about 8.3 million people have the right to vote in the elections in Hungary.
"Everyone should go to vote because this election determines Hungary's course not for four years but for two generations at least", he said.
Firebrand Prime Minister Orban has clashed repeatedly with other European Union leaders during his last term, especially with regard to the bloc's response to the refugee influx across Europe in 2015 and 2016.
Orban's main challengers are Gergely Karacsony, the candidate of the Socialist and Dialogue parties, and Gabor Vona from the nationalist Jobbik party.
As well as hammering home its anti-immigration message, the government has also pointed 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.
"Hungarian democracy is strong", Gergely Gulyas, the parliament faction leader for Orban's Fidesz party.More news: Arsenal 3-2 Southampton: Gunners rated and slated in Emirates thriller
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Analysts, however, were more cautious about the significance of the turnout.
Boros said in a tweet: "The Hungarian political landscape will dramatically change today". Voter turnout was estimated between 64 and 68 percent.
Orban himself voted early on Sunday morning with his wife at a school in the leafy Zugliget suburb of Budapest.
On Origo.hu, a formerly independent website now owned by government allies, stories promoted Orban while also focusing on migration, The headlines included "Migrant gangs fought in England", "They can't stand it anymore in Sweden: They've had enough of migrants", and "A migrant in underpants beat a German retiree half to death".
The leader of Hungary's right-wing nationalist Jobbik party says he expects a "surprise" result in the parliamentary elections.
Orban accuses Soros and the organisations he funds of promoting mass Muslim and African immigration into Europe in order to undermine its Christian identity.
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 is not clear how much impact that will have.
Uncertainties about Orban's expected 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. Another 93 seats will be distributed based on votes for entire party lists.