Seven dead in Egypt protests
Clouds of teargas filled the air. At one point, riot police used one of the incendiaries thrown at them to set ablaze at least two tents erected by youths, a Reuters witness said.
Skirmishes between stone-throwing youths and the police continued in streets around the square into the day. Ambulances ferried away a steady stream of casualties.
Protesters echoed the chants of 2011's historic 18-day uprising. "The people want to bring down the regime," they chanted. "Leave! Leave! Leave!" chanted others as they marched towards the square.
"We are not here to celebrate but to force those in power to submit to the will of the people. Egypt now must never be like Egypt during Mubarak's rule," said Mohamed Fahmy, an activist.
There were similar scenes in Suez and Alexandria, where protesters and riot police clashed near local government offices. Black smoke billowed from tyres set ablaze by youths.
In Cairo, police fired teargas to disperse a few dozen protesters trying to remove barbed-wire barriers protecting the presidential palace, witnesses said. A few masked men got as far as the gates before they were beaten back.
Teargas was also fired at protesters who tried to remove metal barriers outside the state television building.
Outside Cairo, protesters broke into the offices of provincial governors in Ismailia and Kafr el-Sheikh in the Nile Delta. A local government building was torched in the Nile Delta city of al-Mahalla al-Kubra.
With an eye on parliamentary elections likely to begin in April, the Brotherhood marked the anniversary with a charity drive across the nation. It plans to deliver medical aid to one million people and distribute affordable basic foodstuffs.
Writing in Al-Ahram, Egypt's flagship state-run daily, Brotherhood leader Mohamed Badie said the country was in need of "practical, serious competition" to reform the corrupt state left by the Mubarak era.
"The differences of opinion and vision that Egypt is passing through is a characteristic at the core of transitions from dictatorship to democracy, and clearly expresses the variety of Egyptian culture," he wrote.
Mr Morsi's opponents say he and his group are seeking to dominate the post-Mubarak order. They accuse him of showing some of the autocratic impulses of the deposed leader by, for example, driving through the new constitution last month.