Troops sealed off the square with tanks and barbed wire, diverting traffic from the central plaza as thousands of Mohammed Morsi's supporters marched there from several districts in the city.
Protesters encircled security forces and army troops guarding the square, prompting other security forces to fire volleys of tear gas to send the demonstrators away.
"Down down with the murderer!" protesters chanted, in reference to Defense Minister and Army Chief Gen Abdel-Fatah el-Sissi, who forced Morsi out of power after millions took to the streets this past summer demanding he step down.
An Associated Press reporter saw protesters pushed away by other Egyptians armed with sticks and bottles who chased them in the streets before the two sides started hurling stones just steps from the Egyptian museum, located at one of the main entrances of the square.
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"We will go protest and take all streets possible," said Mohammed Said, 45, during a march from the Dokki neighborhood to Tahrir. "We will get in Tahrir at any price."
Another rally ended at a Defense Ministry building and a second at Rabaa el-Adawiyah mosque in eastern Cairo, where a pro-Morsi protest camp was violently dismantled on Aug 14.
Protesters flashed four fingers, their symbol in online and street campaigns for demonstrations.
Across the country, similar clashes broke out with police firing tear gas and gunshots in the air as residents and protesters clashed and threw stones at each other.
Egypt's Muslim Brotherhood group, from which Morsi hails, is escalating protests to coincide with commemorations of Egypt's Oct. 6 opening strike in the 1973 war with Israel.