The EFF wanted him to explain what the government was doing to implement free higher education, student command secretary general Piwaba Madokwe told reporters in Johannesburg on Monday.
Secondly, students wanted Nzimande and vice-chancellors to lift the suspensions and expulsions of students with immediate effect.
Thirdly, all workers at tertiary institutions had to be insourced.
"The time for talking with Blade is over. We can't normalise people coming to the podium and insulting students again," student command spokesperson Naledi Chirwa said.
"How do you call students every now and then [to make submissions]. Two years later, you come back and ask how do we address this issue of free education.
"While you say you stand with us in principle, some of these students are suspended. It was an insult."
A Higher Education National Convention in Midrand on Saturday was cancelled after students dressed in EFF regalia refused to let Nzimande speak.
Programme directors ordered everyone out of the venue as chairs and water bottles were thrown around. Nzimande's security guards apparently escorted him out.
One student in a red EFF T-shirt told a convener at the time: "He's not going to say anything we want to hear."
"We collapsed the plenary for our own interests, because many people here aren't here for our interests,amp;" Sharon Letlape, EFF student command treasurer general, later told News24.
'We are ready to sacrifice our lives'
Letlape said the higher education department had failed to provide feedback on submissions that students had made on the possibility of funding free higher education.
Letlape said, based on the programme for the convention, she did not see Nzimande saying when free education would be realised.
"He was only there to infiltrate Fees Must Fall.
"We had to collapse the convention because there was no platform for him to address the three issues, and we were not going to just sit there."
The student command vowed to continue disrupting institutions until Nzimande addressed those three matters.
"Until we get free education now, we will be fighting," deputy secretary general Rendani Nematswerani said.
"As the EFF student command, we have the capacity to change the State. We are ready to be expelled, we are ready to be excluded, we are ready to be arrested. We are ready to sacrifice our lives to change the lives of a black child.
"If the ANC wants to kill us, we are ready. We can deal with them. We want to make sure that we change the situation," Nematswerani said.