In a rejoinder, Hungary's foreign minister Peter Szijjarto described the move as the "petty revenge" of pro-immigration politicians.
"In relation to the 2019 elections to the European Parliament, it would be easy to, say, establish a new formation from like-minded Central European parties - or, indeed, a pan-European anti-immigration formation", he said.
To become the first-ever case of the European Parliament asking EU capitals to launch the punitive mechanism against one of their own, it must win the backing of at least 376 lawmakers and two thirds of the votes cast. An earlier action against Poland was initiated by the European Union executive.
In a Wednesday afternoon press conference following the resolution's adoption, rapporteur Judith Sargentini (Greens, Netherlands) told reporters that she had personally thanked Weber for making his position clear, and for showing that the European Parliament wants action and accountability.
The European Union accuses Budapest in violation of the rule of law, in particular the harassment of non-governmental organizations. The motion, supported by Parliament's civil liberties committee in June, brings up a number of concerns about the functioning of the country's institutions, including problems with the electoral system, independence of the judiciary and the respect for citizens' rights and freedoms.
While Article 7 procedures may deny Hungary its European Union voting rights, it is now unlikely to happen with Poland saying it will not support such moves.
But in practice that is sure to be blocked by Orban's ally, the nationalist government in Poland that is locked in its own dispute with the European Union over undercutting the rule of law.
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"Viktor Orban's government has been leading the charge against European values by silencing independent media, replacing critical judges, and putting academia on a leash", Sargentini said. Though defiant, he was resigned to the outcome, saying the parliament seemed to have already made up its mind.
"So the plan is that if Hungary can not be forced to let in migrants, then it must be stripped of its right to protect its borders", Reuters quoted Orban as saying on state radio.
His refusal to budge this time cost him support in the EPP conservative grouping, which includes German Chancellor Angela Merkel's Christian Democrats, who have criticised some of Orban's policies.
The EPP's leader, Manfred Weber, said he would vote in favor of the motion against Orban's government, whose Fidesz party belongs to his grouping. But a party spokesman said the group was divided about 50-50. The EU cleared the project previous year.
Amnesty International's expert on human rights in the EU, Berber Biala-Hettinga, hailed the vote as "historic".
"The report in front of you insults Hungary and insults the honor of the Hungarian nation", Orban said during the debate to MEPs, meeting for a plenary session in Strasbourg. The message to government is clear: undermining and violating basic rights and values can not go unpunished in Europe, Socialist MEP Istvan Ujhelyi said.