Police units cannot enter the polytechnic under university asylum rules.
Further clashes between police and youths shut down one of Athens' main avenues.
Greek student groups and academics have campaigned for weeks against the government’s plan to amend the constitution to permit the operation of private universities.
Demonstrations were also held in the cities of Patras and Iraklio, backed by unions of university professors, and primary and secondary education teachers.
Another rally was scheduled for the northern port city of Salonika later on Wednesday.
Greece's ruling conservatives and the opposition socialists agree in principle on the amendment, part of a wider overhaul of the constitution.
They assert that the move will improve the quality of university education in Greece.
Worker unions, student groups and left-wing parties disagree, arguing the state should instead devote more funds to public education.
The education amendment is to be voted upon in the spring, but the exact wording will be decided by the parliament elected after the next general election, scheduled for 2008.