Protest leaders called on demonstrators to march to the Republican Guard headquarters, where at least 51 people were killed July 8 in clashes between Morsi supporters and the army, Ahram Online reported.
Marches took place in several locations throughout Cairo and its suburbs, and elsewhere in Egypt.
Soldiers had stopped tens of thousands of Morsi supporters en route from Rabaa Al-Adawiya Mosque to Abbassiya, home of the Defense Ministry.
Anti-Morsi protesters have expressed concern that supporters of the former president will approach Tahrir Square and the presidential palace, raising the possibility of violence, Ahram Online said. Security was beefed up at the square, ground zero for the protests that led to the ouster of long-time Egyptian leader Hosni Mubarak.
"Egyptians participated today after they recognized that [the June 30 protests] were exploited to carry out a coup against the democratic course, and that their freedom, dignity and right to choose have been attacked," Muslim Brotherhood spokesman Uasser Mehrez said Friday.
Morsi, a member of the Muslim Brotherhood, was the country's first democratically elected president.
Ahead of Friday's demonstrations, interim Egyptian President Adly Mansour pledged a "battle for security to the end" against those he said wanted to push the country into chaos, Voice of America reported.
"I reaffirm to you all my commitment and the government's commitment to restore security and stability in our country," Mansour said in a televised speech Thursday. "We will not be scared or alarmed, and we will not go easy on those who kill the innocent. We will fight a battle of security to the end, we will protect the revolution, we will build the nation and we will move forward without hesitation."