Orban has vowed to continue fighting against the European Union quota on refugees, a plan meant to relocate asylum seekers across Europe.
Casting her vote at the same polling station, retired kindergarten worker Zsuzsanna Draxler said: "Of course I hope the Orban government will be able to continue its work".
"Voter turnout is at record high", tweeted Tamas Boros, co-director of the Policy Solutions think-tank.
The leader of Hungary's right-wing nationalist Jobbik party says he expects a "surprise" result in the parliamentary elections.
Long lines of voters were reported at the Hungarian embassies in London and Paris.
"I think this will be the most frenzied elections Hungary has had [since the fall of communism in 1989]", Bulcsu Hunyadi, a senior analyst at the Political Capital Institute think tank, told Al Jazeera.
Turnout reached 68.13 percent by 1630 GMT, data from the National Election Office showed.
"We are celebrating democracy and it seems like this feast will be handsome because many of us are taking part", said Gergely Karacsony, the leading candidate of the left-wing Socialist and Dialogue parties. He had always voted for Fidesz and praised Orban's policy to support families. "The Hungarian political landscape will dramatically change today".
I only spoke with him twice - De Bruyne on time under Mourinho
United have won their last four league games, their best run since a six-game streak from December 2016 to January 2017. It is the first time he plays in Anfield, in his first knockout (phase) in the Champions League.
Clad in a green jacket and white shirt, Jobbik leader Gabor Vona, 39, arrived to vote in the eastern city of Gyongyos, his home town and the district where he is likely to win a seat.
"We are convinced that high turnout definitely reflects. that people want a change in government", Socialist spokeswoman Bernadett Budai was quoted as saying by national news agency MTI.
It said pragmatism was likely to prevail given the importance of European Union structural funds for Hungary which would probably avoid an all-out conflict with the EU.
"Anti-migration sentiment and anti-NGO populist propaganda have already taken the focus from serious issues like healthcare and education".
On Origo.hu, a formerly independent website now owned by government allies, stories promoted Orban while also focusing on migration with headlines like "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".
"My country is very important to me, and I choose it first, but I feel it's important to keep Europe as an entity", he said.
The opposition denies Orban's claims on migration. In some places in Budapest, thousands - in particular students - were still in line at closing time, and voters in parts of southern and western Hungary were also waiting to vote.
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.