Anas al-Beltagy, son of Muslim Brotherhood leader Mohamed al-Beltagy, has held Egypt's defence and interior ministers responsible for the safety of his father.
Defense Minister Abdel Fattah al-Sisi and Interior Minister Mohamed Ibrahim would be responsible, he warned.
Beltagy's mother meanwhile said she is proud of her son and asked him to hold his ground.
On his Facebook page, Anas said on Friday that the detention of his father has been confirmed. He prayed to God to protect the Brotherhood leader while in detention.
"The world saw how the leader of terrorists and the initiator of violence, as the pro-coup media states, was arrested without any resistance amid claims that the [Muslim Brotherhood] possess light and heavy weapons," Anas posted. "Couldn't [Mohamed] Beltagy, who incites violence in Sinai as they claim, have some terrorists protect him? Rather, he was unarmed in the company of former Minister Khaled al-Azhary [when he was arrested]."
Beltagy's mother told the Freedom and Justice Party's website that she is not sad about the arrest of her son.
“The scene of the arrest of Mohamed [al-Beltagy] made me happy, for he is neither a thief nor a killer. My son is brave.”
"The truth will prevail. He sacrificed a lot for Egypt and he fought corruption," she said, adding that the charges Beltagy faces are unfounded.
Prosecutors announced Beltagy would be held for 15 days pending investigations. He faces charges of inciting violence related to violent clashes following the overthrow of Mohamed Morsy on 3 July.
Edited translation from Al-Masry Al-Youm
