A police officer said a street vendor was shot dead in clashes between Morsi's Islamist supporters and civilian opponents in the Mediterranean city of Alexandria.
Police arrested the shooter and identified him as a member of Morsi's banned Muslim Brotherhood, the officer said, adding that 25 demonstrators were also rounded up.
Two people were also killed in the canal city of Suez where clashes broke out between Brotherhood supporters, police and residents opposed to the Islamists, medics and security officials said.
The interior ministry said police arrested 169 suspected protesters countrywide.
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The Islamists have organised near daily protests since Morsi's overthrow, often clashing with police and civilian opponents.
At least 17 people were killed across the country on January 3 and more than 100 arrested, as police clamped down on the Brotherhood that has spearheaded the protests.
Last month, the government designated the Brotherhood as a terrorist organisation, outlawing membership in or support for the movement.