Morsi's son Osama gave a rare public speech at one protest Friday in the southern city of Minya, speaking to the crowd through a phone call played over loudspeakers. The son told protesters his imprisoned father supported them "with his heart and in spirit" and called on them to "continue their revolution."
"Be patient," Osama Morsi told the cheering crowd, according to a video played on the Doha-based satellite news channel Al-Jazeera Mubasher Misr. "God is capable. ... Your enemy is weak."
Thousands of protesters marched elsewhere in the country. Some rallies turned into clashes between Morsi supporters and those backing the interim military-backed government.
In Fayoum province, south of Cairo, one person was injured during a pro-Morsi march, according to Egypt's state news agency MENA.
In the Mediterranean city of Alexandria, security forces intervened to break up scuffles between Morsi supporters and local residents who objected to their protest, MENA reported. Those supporting the military also marched in the city.
Security forces also foiled an attempted jailbreak in the city after detainees allegedly started a fire to force officers to open an emergency exit at a police station, MENA reported.
Rallies also took place in several districts of Cairo, including near the constitutional court in the southern part of the capital amid tight security. In the Delta city of Damanhour, civilians clashed with Morsi supporters who chanted anti-military slogans, forcing them to end their rally, the pro-government Al-Ahram newspaper reported on its website.
Armored vehicles and barbed wires sealed off several of the capital's major squares, sites of previous protests. They included Tahrir Square, the epicenter of Egypt's 2011 uprising that forced longtime autocrat Hosni Mubarak from power.
Morsi's supporters repeatedly have tried to rally at Tahrir following the coup that toppled Morsi and the Brotherhood-led government. Earlier this month, 59 protesters were killed in clashes with security forces pushing back a crowd trying to storm Tahrir.
Security, already volatile in Egypt since 2011, has worsened since the coup.
The interim government has launched a major security crackdown on the Brotherhood, arresting nearly 2,000 members, charging its top leaders with inciting murder and violence, and breaking up demonstrations by Morsi supporters with what rights groups call excessive force that has killed hundreds. Morsi himself remains held at an undisclosed location.
The crackdown has not prevented Morsi supporters from holding near-daily protests demanding his return. However, fewer now attend since they regularly descend into violence.
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Associated Press writer Tony G. Gabriel in Cairo contributed to this report.