During the poll -- that began at 6 a.m. and will close at 7 p.m. -- some 8.3 million eligible voters were being consulted on the question: "Do you want the EU to be able to mandate the obligatory resettlement of non-Hungarian citizens into Hungary even without the approval of the National Assembly?"
Hungarian Prime Minister Viktor Orban said it was the "no" vote victory that mattered in a referendum on European Union refugee resettlement quotas, not its validity, Efe news reported.
Orban said after casting his vote that a valid referendum was always better than an invalid one, but the legal consequences of the vote apply.
Orban has promised that if the "no" camp wins, he would create a political framework whereby the Hungarian parliament decides on who comes to live in the country.
He said that whether the referendum was valid or not, if there were more "no" votes than "yes" ones, the parliament would pass the relevant legislation.
Polls suggested that the "no" vote would win, but Hungarian law requires a voter turnout of more than 50 per cent for the result to be deemed valid.
Several polls have indicated a voter turnout of less than the threshold required, with a high level of abstention threatening the validity of the result.
Hungary's centre-left opposition and NGOs beyond the Central European nation have called on voters to abstain, or vote null and void in order for the referendum not to produce a valid result.
Human rights organisations have criticised the referendum, declaring it a way of criminalising refugees.
Hungarian citizens living abroad can only vote at Hungarian embassies or other missions after advance registration. Those ballots will arrive in Hungary later in the week to be counted.
In all, nearly 400,000 migrants passed through Hungary last year, en route to Western Europe, primarily to Germany.
While 174,000 people submitted applications for asylum in Hungary, the rejection rate was over 80 per cent. On the other hand, most of the people whose applications were approved have travelled on to other EU countries.
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