UN Special Rapporteur on extrajudicial, summary or arbitrary executions Agnes Callamard, along with experts in the UN Working Group on Arbitrary Detention, had warned that Morsi was held in such "brutal" conditions during his five-year detention in the Tora prison, that his death "could amount to a state-sanctioned arbitrary killing".
Egypt's first democratically elected civilian president Morsi died in June after collapsing in a Cairo courtroom while on trial.
President Abdel Fattah-al Sisi led the military ouster of the Islamist leader in 2013 when he was head of the army.
Morsi, who belonged to the now outlawed Muslim Brotherhood, was overthrown after a tumultuous year in power. The experts noted Friday that "authorities were warned repeatedly" about his deteriorating health to the "point of killing him".
He spent nearly six years in solitary confinement where the panel said he "was denied life-saving and ongoing care for his diabetes and high blood pressure".
But speaking on the sidelines of a review of Egypt's rights record before the UN in Geneva, Marwan told AFP that Callamard had "committed a violation" of UN rules of engagement.
This, he said, was because she had requested details from the Egyptian authorities on Morsi's detention conditions, giving them 60 days to respond, but then went ahead and issued her statement "without waiting for the correct information from the authorities".
"That is a violation."
He said he would leave it up to UN authorities to determine whether or not she should be asked to resign.
In the meantime, he said, "the public prosecutor is investigating the conditions of the death of the former president."
"They are hearing witnesses about what happened and they are waiting for the technical results," he said, adding that the authorities would "publish the results of the investigation."
Reached by phone, Callamard flatly rejected the minister's charge that she had done anything wrong.
"The notion that I did not work according to the rules ... indicates that the minister ... is not knowledgeable about the rules governing the working methods of special rapporteurs," she told AFP.
She acknowledged that she had sent a communication giving Cairo two months to respond, "but we have the right, and in fact I would say the obligation, to speak publicly before those 60 days if we think it is urgent and a matter of life and death".
Callamard stressed that while it was no longer an issue of life and death for Morsi "it is for the hundreds of thousands of other detainees that are facing the similar conditions".
"Waiting 60 days knowing that many more can die and will die if those conditions are not addressed, would have been irresponsible on my part as a special rapporteur."
She said UN experts are required to provide countries with at least 48-hour notice before issuing a public communication about them, and that she had given Cairo a full week.