Morsi’s family has accused the army of abducting him without a cause or reason.
His daughter Shaimaa told a news conference in Cairo that the family was taking legal measures against the army.
Morsi has been held at an undisclosed location without charge since he was removed from power on 3 July.
Morsi’s family said it held the military responsible for the former leader's "safety and security" and that it is taking legal measures against the army.
"We are taking local and international legal measures against Abdul Fattah al-Sisi, the leader of the bloody military coup, and his putschist group," Shaimaa Morsi told reporters.
“We are appealing to the International Criminal Court to launch an investigation into the events leading up to his removal from power.”
Osama, one of Morsi’s sons, said that "what is going on is a violation of human rights and a scandal in every sense of the word."
He described the manner in which the military were holding Morsi as an "abduction".
“We have not had any contact with him since he was abducted by the army,” said Osama.
Mohammed al-Damati, a leading Egyptian lawyer and supporter of Morsi, said it was a breach of the former president's human rights to hold him without charge.
Morsi was ousted early this month after he declined to surrender the presidency to the military.
