"Morsi is under guard at the Republican Guards Club after Wednesday," army spokesman Colonel Ahmed Ali told the Daily News Egypt.
Morsi, 61, was ousted by the powerful military on Wednesday and there were conflicting reports about his whereabouts.
Al-Jazeera broadcast Morsi's interview after Minister of Defence Abdul Fatah Al-Sisi's announcement that he had been ousted.
In the 22-minute video Morsi remained defiant and emphasised his legitimacy saying: "I am the president of the republic and I am keen on this legitimacy."
Media spokesman for the Muslim Brotherhood Gehad El-Haddad first claimed on Twitter that Morsi was under house arrest at the Republican Guards Club.
One hour later he reported that Morsi was transferred to the Ministry of Defence.
Ali warned of conflicting reports and said that if anyone is arrested it will be under the rule of law, adding: "in the new Egypt everything will be done lawfully.
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