Protesters were marching toward military intelligence headquarters, the interior minister's home and on a highway to the airport, the BBC reported.
They also demonstrated at the capital, calling for the reinstatement of Morsi, who was removed from office July 3 amid protests against his administration.
Catherine Ashton, the European Union's foreign policy chief, is in Cairo for talks with leaders of the Muslim Brotherhood -- of which Morsi is a member -- Interim President Adly Mansour and Gen. Fattah al-Sisi, leader of the Egyptian armed forces.
Ashton, in a statement, said she would lobby for a "fully inclusive transition process, taking in all political groups, including the Muslim Brotherhood."
Muslim Brotherhood spokesman Gehad el-Haddaf told the BBC there were no interventions or confrontations with the military at Monday's marches.
On Saturday, more than 70 people died in clashes with the security forces.
Pro-Morsi marchers accused security forces of using excessive force, but the Interior Ministry said protesters opened fire.
Scores of people have died since Morsi's ouster.
Morsi's supporters said another mass demonstration. "Martyrs of the Coup," is planned for Tuesday. They are billing it as a "million-man march."
Protesters were asked to carry coffins "to condemn the use of live ammunition at peaceful demonstrators," said a post on the official Muslim Brotherhood website.
"We call on the great Egyptian people, from all factions, sects and denominations, who refuse the military coup, and all Egyptian families, to come out into the streets and public squares, to reclaim their freedom and dignity, which are being usurped by the bloody coup, and to wrest the rights of the martyrs assassinated by its bullets," the Muslim Brotherhood said.
Ashton arrived in Cairo Sunday. It is her second visit to the country since Morsi's ouster.
In the Sinai Peninsula early Monday, an Egyptian soldier was killed and eight others injured after armed assailants stormed a military post in Rafah, the Middle East News Agency reported.
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