The demonstrators are demanding that the country's military rulers speed up the prosecution of police officers accused of killing hundreds of protesters earlier this year. Those demonstrations led to the ouster of Hosni Mubarak.
This week's violence began Tuesday night. A senior official says more than 1,000 people have been hurt in the recent clashes.
The clashes in Tahrir Square, which began Tuesday night, are the worst since the 18-day uprising.
The violence will likely set back efforts to empower the discredited police to fully take back the city's crime-ridden streets after they melted away during the early days of the Jan. 25 to Feb. 11 uprising.
Additionally, it will almost certainly deepen the distrust felt by many Egyptians toward the 500,000-strong security forces blamed for the worst human rights abuses during Mubarak's 29-year rule. In Washington, U.S. State Department spokesman Mark Toner said the latest unrest "underscores the fact that this is a very difficult period for Egypt."
"It's a period of transition and we remain committed to assisting the people of Egypt as they make their way through this period of democratic transition," Toner said. "Transparency and rule of law are absolutely crucial and violence by any party will not help achieve the goals of the January 25 revolution."
Many Egyptians fear that Islamists are poised to dominate the country, taking advantage of the weakness of liberal and leftist groups born out of the uprising. Others are worried that remnants of Mubarak's regime are undermining the nation.
The Associated Press contributed to this report.