Fayemi, who made the call in a broadcast on Monday, said a Judicial Panel of Inquiry would be constituted to probe the incident, as demanded by student union bodies.
He said the state government would compensensate families of the dead as well as foot the bills of those injured.
The governor also lauded the exoneration of his wife, Bisi, from cause of the deaths.
He said it was wrong for anyone to terminate the lives of students holding a lawful protest over poor electricity supply to their campus.
He said: “I have in the last few days agonised over the incident that took place at FUOYE on Tuesday, Sept 10, 2019
“Until the multiple investigations already set up are completed, I am necessarily constrained from talking about the details of what transpired
“I, however, do not need to be constrained about the emotions a tragedy like this evokes
“Any death is a tragedy. Any shooting arising from legitimate protests diminishes our fledgling democratic dispensation and calls to question, our commitment to fundamental human rights
“Having heard from all parties to the incident, it is pertinent that I now personally convey my deeply felt sorrow for the loss of two promising young lives and for those who suffered injuries
“Our government prides itself on its strict adherence to the rule of law.
“The right of citizens to protest on any issue relating to governmental actions or inactions is a fundamental component of our good governance agenda.
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“We could not therefore under any circumstances, have directed that deadly force be used on any of our citizens freely expressing their right to protest
“Even before the conclusion of the investigations into this matter, we have taken a number of steps; a high level government delegation has visited the families of the deceased.”