The grassroots Tamarod ('Rebellion' in Arabic) movement is driving the protest campaign with a petition of signatures seeking Mursi's ouster and a snap election, which has united liberal and secular opposition groups, including the National Salvation Front.
However, many ordinary Egyptians - angered by Mursi's political and economic policies - are also taking part in the rally.
Opposition activists say more than 22 million people have signed the petition and have urged the signatories to come out in Cairo's Tahrir Square.
The current protests come on the first anniversary of Mursi's election as the country's first Islamist president.
61-year-old Mursi's opponents say he has failed to tackle economic and security problems.
Critics also say he has put the Islamist agenda of his Muslim Brotherhood party ahead of the country's wider interests.
In Cairo, anti-Mursi supporters waving red cards chanted: "Irhal! Irhal!" ("Leave! Leave!").
The rallies from the square and elsewhere in Alexandria are expected to move later in the day to the central Sidi Gaber area.
A big stage has been erected in the city's main square, with protesters checking the identities of those going in and out of the square.
There are similar rallies in Suez, Monofia and Sharqiya - the birthplace of Mursi.
Supporters of the president are also holding their own rallies.
Egyptians have been waiting with anticipation for today's protests for many weeks - the opposition vowing not to leave until Mursi steps down and calls early presidential elections.
But his supporters point out that Mursi was elected and say he should see out his full term in office, indicating a deep split in Egyptian society.
In the tense build up to the protests, at least three people, including a US citizen, died in violence on Friday.
US national Andrew Pochter was killed in the northern city of Alexandria as protesters stormed an office of the Muslim Brotherhood.
Washington has warned Americans not to travel to Egypt.
The UK urged its citizens to "avoid all demonstrations and large gatherings" while France said citizens should "limit movements to those strictly necessary".
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