A protester and a policeman were shot dead in Cairo on Thursday, security sources said, one year after government forces killed hundreds of demonstrators in the worst bloodshed in Egypt's recent history.
The 31-year-old protester died from a bullet wound to the chest during clashes between protesters and police in Giza on the outskirts of the capital, the sources said.
Earlier in the day, gunmen on a motorcycle shot a police officer in the same district.
A top security official in Cairo said 30 members of the Brotherhood were arrested on Thursday for rioting.
Small, hit-and-run demonstrations are the most the group can muster after a fierce security crackdown has seen many thousands arrested and hundreds sentenced to death.
The Brotherhood, once Egypt's most organized political movement, was declared a terrorist organization last year, and its political wing was banned last week.
Violence has polarized Egyptians since the army overthrew elected Islamist President Mohamed Morsi last year following mass protests against his rule.
Hundreds of supporters of Morsi's Muslim Brotherhood have been killed and thousands arrested since he was ousted, with the largest number of deaths occurring one year ago on Thursday, when security forces stormed two protest camps in Cairo.
Militant attacks have also increased since Morsi was toppled, with Sinai Peninsula-based militants killing soldiers and police in an insurgency the government has struggled to quell.
Human Rights Watch said this week that those killings were systematic, ordered by top officials and probably amount to crimes against humanity. The rights campaigning group called for a U.N. inquiry.