Egypt's new prime minister Hazem el-Biblawi previously served as a finance minister and deputy prime minister in the country's interim government after former President Hosni Mubarak stood down in 2011.
According to Egyptian news agency Ahram, the economist resigned over the response to a protest by Coptic Christians which left dozens of the latter dead.
He is also co-founder of the Egyptian Social Democratic Party and served as undersecretary-general at the UN between 1995 and 2000.
The Muslim Brotherhood tells ITV News they are against violence but will "pay the price of their blood" to restore their ousted president.
Egypt's army has named two further officials in the transitional government as its supporters and opponents vowed to stay on the streets.
There has been outrage in Egypt after 51 people were killed near an barracks where ousted President Mohamed Morsi is thought to be held.