The National Election Office initially said it did not intend to disclose any results while voters were still waiting outside polling stations. 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.
Orbán has leaned farther to the right in recent years, becoming one of Europe's most prominent populist voices.
Critics say Orban has put Hungary on an increasingly authoritarian path and his stance on immigration has fueled xenophobia.
Since 400,000 people passed through Hungary in 2015 on their way to Western Europe, Orban has made migration the near-exclusive focus of his government. Despite being tipped to take two-thirds of the 199 parliamentary seats for a third time only months ago, ruling party officials have said that now appears out of reach. Such an outcome would allow Orbán to pursue radical change, perhaps tightening his grip Hungary in the same vein as Poland.
Prime Minister Viktor Orban's Fidesz Party is enjoying wide support with its anti-immigration policy.
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In a Thursday morning tweet, the president credits "the strong immigration laws of Mexico and their willingness to use them". The Pentagon said officials had not yet determined how many troops would be deployed to support border security operations.
Gabor Vona said Sunday he would resign and put his fate in the hands of his party if they don't win but plans to remain in politics nonetheless.
His main challengers are Gergely Karacsony, the candidate of the Socialist and Dialogue parties, and Gabor Vona from the nationalist Jobbik party.
Orban's election campaign focused on his staunch anti-migration policies despite opinion polls suggesting that many Hungarians are actually more anxious about other social concerns such as poverty, corruption and improving funding for the country's ailing health care system.
The election produced a turnout of around 70 percent, exceeding the past three elections.
The anti-immigrant campaign has gone down well with numerous roughly two million core voters of Fidesz.
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Analysts say a high turnout favors the opposition, especially Jobbik.
Jobbik's Mr Vona urged his supporters not to become complacent.
"Migrants should not come here, and this (Fidesz') economic policy should continue", said Janos Dimovics, a pensioner who came from his village to see Orban.
After casting his vote in a wealthy district of Budapest, he said: "From here I will go and take part in mobilizing voters".
Orban, who voted with his wife at a Budapest school near their home, told a crowd of reporters that he will "respect the decision" of the Hungarian voters.
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Asked whether he was fighting the EU he said: "The EU is not in Brussels". Hungary's National Election Office reports 13.17 percent of eligible voters had cast ballots by 9 a.m. (0700GMT). The EU is now in Berlin, in Budapest, in Warsaw, in Prague and at Bucharest.