Troops and police took relatively low-key security measures before the Friday of Martyrs processions that were to have begun from 28 mosques in the capital after weekly prayers.
But midday prayers were cancelled at some mosques and there were few signs of major demonstrations unfolding in Cairo.
Egypt has endured the bloodiest civil unrest in its modern history since August 14, when police destroyed protest camps set up by Mr Mursi's supporters in Cairo to demand his reinstatement.
The violence has alarmed Egypt's Western allies but US President Barack Obama acknowledged that even a decision to cut off US aid to Cairo might not influence its military rulers. He said the US was re-evaluating its ties with Egypt, adding: "There's no doubt we can't return to business as usual, given what's happened."
The US has nurtured an alliance with Egypt since it signed a peace treaty with Israel in 1979.
Military cooperation includes privileged US access to the Suez Canal.
The Brotherhood, hounded by Egypt's new army-backed rulers, had called for demonstrations across the country against the crackdown, testing the resilience of its battered support base.
Security forces kept a watchful eye but did not flood the streets, even near Cairo's central Fateh mosque where gun battles killed scores of people last Friday and Saturday.
Hosni Mubarak, the ex-military former president toppled in 2011, was freed from jail on Thursday in a symbolic victory for the army, while Mr Mursi remains behind bars.