The marchers included students and staff of the university, many wearing the blue of the CEU and some waving Hungarian, EU as well as US flags as they marched from the historic Buda castle to the parliament building in Budapest.
Organisers said up to 80,000 people took part in the protest, while an AFP photographer put the number at 60,000.
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The English-language CEU was founded by Hungarian-born billionaire George Soros in the early 1990s, aimed at helping the region's transition from communism to democracy.
The new rules, approved by parliament on Tuesday, bar institutions based outside the European Union from awarding Hungarian diplomas without an agreement between national governments.
They will also be required to have a campus and faculties in their home country -- conditions not met by the CEU, which is registered in the United States.
The legislation has attracted widespread criticism abroad, including from Washington, Brussels and academics. There were also street protests last Sunday and on Tuesday.
The US State Department earlier this month called for the proposal to be withdrawn, while an open letter has been signed by over 900 academics around the world including 18 Nobel prize-winning economists.
"I have no children, but the way they adopted the regulations against this university is frightening," Gabor Kis, 45, a cook, told AFP during the protest on Sunday.
"If they can do that to CEU, they can do whatever they want! This has to stop!"
The legislation, which still has to be signed into law by the president, does not mention the CEU by name but the university sees itself as the main target and has warned it may have to close.
Critics see the move as another attack by Prime Minister Viktor Orban on Soros, whom he accuses of seeking to meddle in politics and undermine Europe by promoting immigration into Europe.
Last week the government published legislation that will oblige NGOs receiving above a certain amount of foreign funding to register and stamp any publication with "foreign-funded organisation".
Mirroring similar rules in Russia, this is also seen as targeting Soros's Open Society Foundation which funds civil society groups and which has also come under fire elsewhere in the region.
Government spokesman Zoltan Kovacs denied in a blog post on Thursday that the CEU was being singled out, saying that irregularities had been found with 27 foreign higher education institutions.
"It's noteworthy that all of the other institutions have accepted this modest minimal condition of university equality and fairness. Only CEU has protested because the university insists on its unfair privileges," Kovacs said.
"These people at the top, they don't realise that we don't live in Russia, but in Hungary!" another protester, 23-year-old IT expert Viktor Szakal, told AFP.
"We have to show strength with our numbers. I'm glad that so many people showed up. Orban understands only the rules of power, and our power comes from our numbers."
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Orban has said he is prepared "to negotiate with the United States" on the future of the university which has until January to conform with the new law.
The CEU has 1,800 students from 100 countries and is ranked in the top 50 universities for political and international studies in the World University Rankings list.
The demonstration was the biggest since 2014 when protesters opposed Orban's right-wing government over a tax on internet usage, which was later withdrawn.
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