The violence — the worst in Cairo since troops killed 51 Morsi supporters on July 8 — came as a senior U.S. diplomat was visiting the Egyptian capital.
Representatives of Tamarod, the movement responsible for mobilizing massive protests that resulted in Mr. Morsi's ouster, have refused to meet with Deputy Secretary of State William J. Burns. The group said it rejects interference by external powers in Egyptian affairs.
Mr. Burns said that only Egyptians can determine their future.
"I did not come with American solutions, nor did I come to lecture anyone," said Mr. Burns, the highest-ranking U.S. official to visit the North African country since Mr. Morsi was deposed.
The ultraconservative Salafist Nour Party, which had backed Mr. Morsi's ouster, also has declined to meet with the U.S. diplomat.
Mr. Morsi has been held at an undisclosed location since his ouster on July 3. The military-backed interim administration has issued arrest warrants for Muslim Brotherhood leaders and has frozen their assets, accusing the Islamists of inciting violence.
Mr. Burns said the military must avoid any "politically motivated arrests."
"If representatives of some of the largest parties in Egypt are detained or excluded, how are dialogue and participation possible?" he said Monday in Cairo.
Muslim Brotherhood spokesman Gehad El-Haddad said on Twitter that Mr. Burns' calls for inclusion fall on the "deaf ears" in the military.
Mr. Burns has met interim President Adly Mansour; interim Prime Minister Hazem el-Beblawi; interim Vice President Mohamed ElBaradei; and Gen. Abdel-Fattah El-Sissi, the defense chief.