The students arrived in the capital, Colombo, accompanied by trade union and rights activists and opposition politicians, and rallied in front of the main railroad station.
The issue has sparked months of demonstrations in the island nation, with doctors and students urging the government to shut down the private South Asian Institute of Technology and Medicine, the only private university training medical students.
Rathkarawwe Jinarathana, a Buddhist monk and student leader, said the government wants to privatize education and weaken state-funded education and health services.
There was no immediate response from the government to the protest.
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Students at state-run schools say the private medical school does not meet the country's educational standards. The institute says its standards and facilities are better than those at state-run universities. A legal battle has been continuing since last year over whether to allow graduates of the university to work as doctors.
For more than half a century, Sri Lanka has provided free education through the university level. Private schools also exist, but the South Asian Institute of Technology and Medicine is the only private medical school.
A private medical university that opened in the 1980s was acquired by the government due to student protests.