* Authorities and Brotherhood blame each other for violence
* Unrest follows sentencing of over 500 Islamists to death
* Army chief who deposed Mursi to run for president (Adds detail)
CAIRO, March 28 (Reuters) - At least three people were killed in clashes in Cairo on Friday amid protests by the Muslim Brotherhood, days after hundreds of its Islamist supporters were sentenced to death, official sources said.
Newspaper Al Dustour said on its website Mayada Ashraf, one of its journalists, had died covering fighting which security sources said had involved Brotherhood supporters, security forces and residents.
Another website posted footage of a seemingly unconscious woman with a bloodstained face being carried down a street, identifying her as the journalist. The authenticity of the video could not be independently verified.
Security sources said birdshot had been fired during the clashes. A health ministry official, who declined to be named, said three people had been killed and at least one of those died from live ammunition.
State-run news agency MENA quoted an unnamed interior ministry official as saying four citizens were killed in the clashes, blaming Brotherhood supporters for the deaths. It added nine Brotherhood supporters suspected of opening fire on citizens had been detained.
The Brotherhood's Freedom and Justice party published a statement on its Facebook page blaming security forces for the death of the journalist.
Hundreds of Brotherhood supporters took to the streets in scattered protests across Egypt on Friday, in some instances throwing missiles at police who fired tear gas.
Abdel Fattah al-Sisi, who deposed elected Islamist President Mohamed Mursi in July after mass protests, announced on Wednesday his resignation as army chief and his intention to run in presidential elections that he is widely expected to win.
Supporters of Mursi's Brotherhood, outlawed and branded a terrorist group by the army-backed authorities, see Sisi as the leader of a coup against a democratically elected president.
Since Mursi's overthrow the authorities have staged a crackdown on the Brotherhood, killing hundreds and arresting thousands, including most of its top leaders. The Brotherhood says it is committed to peaceful activism.
A court sentenced more than 500 Brotherhood supporters to death on Monday, triggering clashes between security forces and protesters in which at least one man was killed on Wednesday.
Egypt has seen three years of political turmoil since an uprising ended Hosni Mubarak's three decades of one-man rule. (Reporting by Shadia Nasralla; editing by Andrew Roche)