Opposition protesters threw Molotov cocktails in a clash with police Friday evening at the presidential palace, Ahram Online reported. Security was tightened at the palace in advance of the demonstration.
At the university, Mohamed El-Omda, an independent member of Parliament who has close ties with the Muslim Brotherhood, addressed the crowd.
"Some people may want to tell the outside world that the people are against legitimacy," he said. "But the Egyptian people won't turn against a presidency they elected and a Shura Council they voted for."
The "All Against Violence" demonstration was organized by the Islamist Al-Gamaa Al-Islamiya and its political arm, the Construction and Development Party. The Muslim Brotherhood said it would have a "symbolic presence."
Some of the speakers anticipated a time when all political activists in Egypt will be Islamists.
"Soon those ruling and the opposition will be from the Islamist current. This is Egypt's nature," said Ahmed Aref, a Muslim Brotherhood spokesman.