Protesters fear that a new board of trustees at the University of Theater and Film Arts, headed by an ally of Prime Minister Viktor Orban, will ruin its autonomy.
The students have occupied the campus for a week.
Orban supporters say the arts are dominated by liberals and leftists.
The university is the seventh institution to be transferred under the control of private foundations where the board of directors is chosen by the government.
The government denies claims that it restricts free speech and says privatizing this university and others will make them more competitive.
On Sunday, the Human Chain hosted four other institutions and linked around 8,000 protesters from parliament to the university. The demonstrators demanded the autonomy of the school and the freedom of artistic activity and education.
Marta Barbarics, who attended the rally, told Reuters news agency: “For a university, being able to function independently is the foundation of democracy. “
She added, “If a university cannot teach in a way that its citizens deem appropriate, then there are serious problems and the leadership of a university does not quit without reason. “
The University of Theater and Film Arts has nurtured some of the big names in Hungarian cinema. Graduates from the university include Oscar-winning director István Szabó – whose credits include Mephisto – and actress Alexandra Borbély.
The students have occupied the university since last Sunday.
The new head of the board, Attila Vidnyanszky, said on Tuesday he was open to dialogue. However, he also said he wanted “a different kind of thinking” at the university, adding that existing courses would be maintained with an emphasis on patriotism and Christianity.
Fears for artistic and academic freedom in the country have intensified in recent years.
In 2019, the Central European University of Budapest moved most of its courses to Vienna after a legal battle launched by Mr Orban. The university said it could no longer “function as a free institution” in Budapest.
In July, more than 70 journalists and employees of the main Hungarian news site Index resigned.