During a news conference, Morsi's daughter, Shaimaa, criticized the military's role in what she called a military coup led by Defense Minister Abdel Fattah El-Sisi and the "kidnapping" of her father, Ahram Online reported.
Morsi, the first democratically elected president in Egypt, was unseated July 3 and has been in an undisclosed location since.
"I hold El-Sisi responsible for anything that happens to my father's health while he is in captivity," she said, calling his detention as "a criminal act against human rights."
Accompanying his daughter were Morsi's sons Osama and Abdallah.
Osama Morsi suggested El-Sisi could face repercussions for the "crime he committed against democracy" and that his family might seek help from the International Criminal Court in The Hague, Netherlands.
Also Monday, Gehad El-Haddad, spokesman of the Muslim Brotherhood's Freedom and Justice Party, denied reports Morsi was on a hunger strike to protest detention, noting that information about Morsi and his whereabouts was unavailable and there has been no communication with him since he was ousted.
"Even the [European Union] is concerned about Morsi's captivity and health illustrated by [EU foreign chief] Catherine Ashton's recent visit demanding his release," said Mohamed El-Damaty, head of the lawyers syndicate freedoms committee and a member of the syndicate's board.
Clashes between opponents and supporters of ousted President Mohamed Morsi killed at least three people and wounded more than 100 others across Egypt Sunday, officials said.
In Mansoura Sunday, officials said three people died in a confrontation of pro- and anti-Morsi groups, Ahram Online reported.
Clashes in Suez erupted during when Morsi backers entered the city's al-Arbaeen Square, scene of opposition rallies since the 2011 revolution that chased Hosni Mubarak from office, state news agency MENA said.
Medical officials said 112 people were wounded.