Morsi was overthrown along with his Brotherhood-led government after millions protested against his leadership, claiming the Islamist president was incompetent and overstepped his authority during a year in power.
Since then, Brotherhood supporters have staged near-daily rallies around the country, protesting security crackdown in which hundreds have been killed and more than 2,000 of group's members have been jailed. Morsi has been held incommunicado since his ousting and a court has ordered an outright ban on his group.
Authorities appear to have expanded the scope of the crackdown. A police officer was suspended from his duties in the Nile province of Gharbiya, north of Cairo, because he was suspected of being a Brotherhood member, security officials said Friday. The officials spoke on condition of anonymity because they were not authorized to talk to journalists.
The decision could signal that the military-backed leadership will purge Brotherhood members from the security forces, a move that could deepen tensions. Morsi supporters and those backing the military already accuse each other using violence to advance their causes.
Although Brotherhood supporters have been staging rallies regularly since the overthrow, their numbers have been dwindling on the streets of Cairo as the security forces crack down and authorities fortify government institutions and the capital's major squares.
Egypt's riot police smashed two protest camps of Morsi supporters in mid-August, killing hundreds of protesters and touching off days of the deadliest violence since the country's Arab Spring protests.
While the Brotherhood's ranks appear to have thinned since, the resolve of those still protesting remains firm.
"I am here protesting because the country is being stolen," said Mohammed Kassam, a university professor who attended a protest Friday in Cairo. "There are people who have the arms and the tanks and want to oppress people and impose their will on them."
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Associated Press writers Barbara Surk and Mariam Rizk contributed to this report.