"We will develop new peaceful means of protest that will take them all by surprise," union spokesman Abdallah al-Mahi told Anadolu Agency.
He added that planned protests would "not be confined to the university campus."
On Wednesday, security forces entered the Azhar University's Cairo campus following an appeal from University President Osama al-Abd for police intervention to stop "rioting" students.
Earlier the same day, student protesters had stormed the university's administrative building, trapping al-Abd and other university officials inside.
The move followed clashes outside the building between students and administrative security personnel.
The student union accuses the university's administration of turning the campus into a "military barracks" and putting students at the mercy of security forces with the blessing of Al-Azhar Grand Imam Ahmed al-Tayeb.
Al-Azhar University security chief Mahmoud Sobeih claimed police had found some students in possession of "bladed weapons."
Al-Mahi, for his part, asserted that "suspicious elements" had tried to infiltrate the rallies in a bid to tarnish the image of the student protests.
"This is a farce," he said defiantly. "It will not force us to give up our struggle."
The "Students against the Coup" movement, comprised of university students opposed to the July 3 ouster of elected president Mohamed Morsi by the military, had earlier accused the university's security staff of hiring thugs to "infiltrate protests" and using birdshot to disperse student rallies.
"Following an initial investigation, it turned out that the shooters, who were not university students, had aimed to drag protesters into violence," the movement declared on its Facebook page.
It went on to denounce the recent clashes on the Azhar University campus, reaffirming its commitment to peaceful protest.
Pro-democracy demonstrations have rocked several universities throughout the country since the academic year began in September.
The most violent of these have been seen at Al-Azhar University's Cairo campus, where the academic year began two weeks ago after having been postponed by almost one month.
Egypt has remained in a state of turmoil since the powerful military deposed democratically-elected Morsi on July 3 following massive protests against his presidency.
