Haddad's father, Essam El-Haddad, widely seen as Morsi's right-hand man, was among those held, he added.
A military spokesman did not respond to requests for confirmation of Morsi's detention, and it was not immediately clear whether the ousted president would later be allowed to leave.
His top aides have switched off their phones. Other presidential aides who were separated from Morsi earlier in the day say they have lost communication with their leader.
Morsi had earlier been at his office in the Republican Guard's headquarters, before he was moved.
A police general told AFP that security forces were seeking to arrest leaders of his Muslim Brotherhood movement.
Police have already arrested Saad al-Katatni, head of Morsi's Freedom and Justice Party, and Rashad Bayoumi, the Muslim Brotherhood's deputy supreme guide, the general said.
Hours after the military announced it had cancelled the constitution and would appoint the head of Egypt's top court as interim president, Morsi issued a defiant call to arms in a prerecorded speech aired on Al-Jazeera television.
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A military spokesman did not respond to requests for confirmation of Morsi's detention, and it was not immediately clear whether the ousted president would later be allowed to leave.
His top aides have switched off their phones. Other presidential aides who were separated from Morsi earlier in the day say they have lost communication with their leader.
Morsi had earlier been at his office in the Republican Guard's headquarters, before he was moved.
A police general told AFP that security forces were seeking to arrest leaders of his Muslim Brotherhood movement.
Police have already arrested Saad al-Katatni, head of Morsi's Freedom and Justice Party, and Rashad Bayoumi, the Muslim Brotherhood's deputy supreme guide, the general said.
Hours after the military announced it had cancelled the constitution and would appoint the head of Egypt's top court as interim president, Morsi issued a defiant call to arms in a prerecorded speech aired on Al-Jazeera television.
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