New rules introduced by the government mean the Central European University (CEU) would be unable to award diplomas because it is registered in the US.
The university was founded by philanthropist George Soros.
The legislation has already been rushed through parliament.
Demonstrators in the capital on Sunday want President Janos Ader not to sign the controversial legislation backed by the governing right wing Fidesz party of Prime Minister Viktor Orban.
At the scene: The BBC’s Erika Benke in Budapest
Unlike last Sunday’s protest, it was not just students who were out in the street – there were also lots of families, with some middle-aged and some elderly people in the crowd.
They marched peacefully in the bright spring sunshine, crossing Budapest’s historic Chain Bridge as they headed towards Parliament. The protesters chanted slogans urging President Janos Ader to ask the Constitutional Court to review the new law adopted by parliament last week that is likely to lead to the closure of the CEU.
BBC Budapest correspondent Nick Thorpe says it was probably the biggest anti-government protest in Budapest since Mr Orban came to power seven years ago.
The government passed amendments to the Higher Education Act last week which would make it impossible for the CEU to continue working in Budapest – 26 years after it was set up by Hungarian-born billionaire financier and philanthropist George Soros.
The government opposes the liberal outlook of both the university and many non-governmental organisations.
Mr Soros has a strained relationship with Mr Orban – a keen supporter of US President Donald Trump – who has accused the financier of wanting a role in Hungarian politics and supporting the influx of migrants into Europe.
Mr Orban recently claimed Hungary was “under siege” from asylum seekers.
The Central European University
- Founded to “resuscitate and revive intellectual freedom” in parts of Europe that had endured the “horrific ideologies” of communism and fascism
- Occupies a building that began as an aristocrat’s palace before becoming state-owned offices for a planned socialist economy
- Has 1,440 students – 335 from Hungary and the rest from 107 other countries
- Presents itself as a champion of free speech, with links to universities in Russia, Kyrgyzstan, Georgia and Kazakhstan