Morsi has not been charged with a crime, but arrest warrants have been issued for hundreds of his fellow Muslim Brotherhood members and their supporters, The Washington Post reported Wednesday.
Morsi, like Hosni Mubarak before him, has been accused of using the country's judicial system to punish opponents. Human rights groups say the new government is doing the same thing.
A neutral judiciary is one of the greatest casualties of the turmoil in Egypt over the last few years, said Heba Morayef of Human Rights Watch.
"In the last few days, that tradition continues," she said.
The families of missing Brotherhood leaders have been unable to contact them, said a relative of a Morsi aide who disappeared the night of the ouster.
The relative said the missing family member has been allowed a few phone calls, but provided other few details.
"We don't have any information on who's detaining them," the relative said.
Badr Abdelatty, a spoken for the foreign affairs ministry, denied any crackdown on the Muslim Brotherhood, saying there are "no exceptional measures being taken against any political force."
Mohammed Badie, the group's spiritual leader, and nine other Islamist leaders are accused of inciting violence in which 50 pro-Morsi supporters were killed by security forces Monday.