The National Election Office initially said it did not intend to disclose any results while voters were still waiting outside polling stations.
A man in the capital, Budapest, said he hopes the ruling party will win.
Mr Orban claims the opposition - collaborating with the United Nations, the European Union and wealthy philanthropist George Soros - wants to turn Hungary into an "immigrant country", threatening its security and Christian identity.
Hungarians voted in large numbers Sunday in an election that is being keenly watched across Europe, with firebrand nationalist Prime Minister Viktor Orban tipped to win a third consecutive term and press ahead with his anti-immigration agenda. That was the highest turnout figure at that time since at least 1998. In contrast, the turnout was only 61.7 percent in the last election, in 2014, which gave him a massive victory. "Opposition politicians are right to be glad about high turnout, but it does not mean that anything has been decided".
Boros said in a tweet: "The Hungarian political landscape will dramatically change today". The opposition Socialist Party urged authorities to "at least distribute water" in districts where voters were waiting in line for hours.
About 8.3 million Hungarians are eligible to vote this election, and preliminary results are expected Sunday night.
All 199 seats in the Hungarian parliament are up for grabs, with the opposition keen to make sure Mr Orban's bloc does not win a super-majority which would allow the autocratic leader to push through further constitutional changes.
"This is a country which has always stepped up for itself, so we can trust in the people, I will accept their decision", he said.
Gabor Vona of the nationalist Jobbik party urged his supporters not to become complacent. In Hodmezovasarhely, a Fidesz stronghold in southeastern Hungary, voters complaining of graft, cronyism, and intimidation elected an independent in a February mayoral election for the first time in two decades. According to the National Election Office, 13.17 percent of eligible voters had cast ballots by 9 a.m. (0700GMT), while in 2006 turnout was 11.39 percent at the same hour.
'We are celebrating democracy and it seems like this feast will be attractive because many of us are taking part, ' said Gergely Karacsony, the leading candidate of the left-wing Socialist and Dialogue parties.
Uncertainties about Orban's 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.
Orban told reporters after casting his ballot that he is fighting for the future of his beloved country.
Orban and his wife voted early in the morning at a school in the leafy Zugliget suburb of Budapest.
Speaking at a recent campaign rally, Orban accused the European Union of "trying to take away our country". The EU is in Berlin, in Budapest, in Warsaw, in Prague and in Bucharest.