Supporters of deposed Islamist president Mohamed Morsi, overthrown in a July military coup, tried to converge on a central Cairo square for the anniversary celebrations, when police confronted them.
At least 30 people were killed in Cairo, and four south of the capital, and 209 people were wounded, senior health ministry official Khaled al-Khatib said in a statement.
An interior ministry official told AFP no policemen were killed in the clashes.
Three months after Morsi's overthrow, followed by a harsh crackdown on his Muslim Brotherhood movement, the Islamists had planned to galvanise their protest movement in a symbolic attempt to reach Tahrir Square.
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Today's death toll was the highest in clashes between Islamists and police since several days of violence starting on August 14 killed more than 1,000 people, mostly Islamists.
After several weeks of relative calm, the Islamists said they would escalate their protests by trying to rally in the symbolic Tahrir Square.
Several thousand people, some carrying pictures of army chief Abdel Fattah al-Sisi, waved Egyptian flags as warplanes flew overhead in formation and patriotic songs blared from loudspeakers.
Elsewhere in the city, the air was thick with tear gas and the crackle of gunfire as police confronted several marches heading for Tahrir.
Clashes also erupted in the Suez Canal city of Ismailiya, a security official said.