Erdogan spoke during a meeting with a group of foreign journalists a day after he claimed that Morsi didn't die of natural causes but was killed.
He compared Morsi's death to the brutal killing of Saudi columnist Jamal Khashoggi, slain killed at the Saudi Consulate in Istanbul in October.
"In the same way that we didn't allow the murder of the late Jamal Khashoggi to be forgotten, we will never allow Morsi's drama to be forgotten," Erdogan said.
The Turkish leader, who is a fierce critic of Egyptian President Abdel-Fattah el-Sissi, added that he believed that the United Nations should take up "Morsi's suspicious death."
In Cairo, Egyptian Foreign Minister Sameh Shoukry lashed out at Erdogan, saying the latest stream of his remarks reveal the depth of his ties to the Muslim Brotherhood, a pan-Arab movement that Egypt has banned as a terrorist group.
Morsi, Egypt's first democratically elected president who hailed from the now outlawed Brotherhood, was ousted by the military in 2013 after massive protests against his divisive rule. The authorities subsequently launched a major crackdown on the Brotherhood, arresting Morsi and many others of the group's leaders.
Morsi collapsed and died in a Cairo courtroom on Monday.
His death drew criticism from international and local human rights groups, which accused the Egyptian government of deliberately denying Morsi access to medical care in jail.
A statement Thursday by Shoukry accused Erdogan of spreading "extremist thought."
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