Orban was summoned to a meeting with top officials from the European People's Party (EPP) over the law that could force the closure of a Budapest university founded by US billionaire George Soros.
The European Commission on Wednesday launched legal action against Hungary over the issue, giving the government one month to comply or face being taken to court.
"Prime Minister Viktor Orban pledged in the EPP council to follow and carry out all the demands of the European Commission within the timeframe set by the Commission," said Siegfried Muresan, a spokesman for EPP President Joseph Daul.
Daul said in a statement that the EPP "sent a clear message to prime minister Orban and to his member party, Fidesz, that we will not accept that any basic freedoms are restricted or that the rule of law is disregarded.
"The EPP demanded from Fidesz and from the Hungarian authorities that they take all necessary steps to comply with the commission's request. Prime Minister Orban has reassured the EPP that Hungary will act accordingly."
The EPP insisted that the Central European University remain open and all action against it be withdrawn.
The commission, the executive of the 28-nation EU, on Wednesday launched so-called infringement action against Hungary over the law targeting the university, alleging breaches of fundamental EU free market laws.
Hungary can be taken to the European Court of Justice if it fails to comply. The court can impose stiff financial penalties.
Orban's cabinet chief Antal Rogan told Hungarian public television later that "Orban made clear during the meeting that we believe that no legal modification threatens the presence of the Soros-founded CEU operation in Hungary."
Orban added that university's "freedom of education and scientific research is ensured" and that "the university can launch its new academic year," Rogan said.
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