Opposition groups have expressed frustration with Morsi, who marks his first year in office next month. He's the first democratically elected president in Egyptian history.
Criticism against his administration ranges from his oversight of a weak economy to the perceived monopolization of power by Islamic politicians.
Demonstrators Friday said there were several hundred protesters who turned out for three separate marches through downtown Cairo, Egyptian news agency al-Ahram reports.
Security around government buildings in Cairo is tight.
Friday's demonstrations were billed as million-man marches. Opposition groups are trying to get 15 million signatures by June 30 to force an early election.
Protesters in Alexandria chanted slogans against the Muslim Brotherhood, the president's political support group.
The U.S. State Department issued a travel advisory earlier this week warning of the security risk in Egypt.
"Political unrest ... is likely to continue in the near future," a State Department warning read.
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