The EU has expressed fears that Hungary is undermining academic freedom, non-government organisations and the rights of asylum seekers.
"The College will review all these issues closely when it takes the next round of infringement decisions at the end of April," European Commission First Vice President Frans Timmermans said, referring to an EU Commission body.
"Wherever individual cases are legally mature and our legal concerns remain unaddressed, we will move to the next steps," he told a press conference.
If launched, such proceedings involve long series of consultations to determine if EU laws have been breached. If needed, the Commission can refer cases to the European Court of Justice, which could impose fines.
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But Timmermans said the Commission wants for now to pursue a political dialogue to resolve the points of contention and determine what Hungarian Prime Minister Viktor Orban's views are on the rule of law.
Timmermans, the Dutch right-hand man of Commission chief Jean-Claude Juncker, said not only is Orban open to such a dialogue, but "in the view of the Commission today, there is not a systemic threat to the rule of law in Hungary."
It started a long process which could eventually see Warsaw's voting rights suspended in the Council of Ministers, the EU's highest decision-making body.
Commission head Jean-Claude Juncker has criticised Hungarian legislation that could force the closure of the Central European University in Budapest founded by US billionaire investor George Soros.
He has also lashed out at the Orban government for posting questionnaires titled "Let's stop Brussels!" to households nationwide asking them how to deal with EU policies that it says threaten their independence.
Failure to comply could result in the closure of the organisations.