Mohammed ElBaradei, a former UN nuclear agency chief, was named Egypt's interim prime minister on Saturday.
Interim head of state Adli Mansour was installed on Thursday to oversee a military roadmap to elections, the day after the army overthrew Islamist President Mohammed Morsi.
ElBaradei was among liberal leaders who opposed Morsi and called for the massive protests that showed how the Muslim Brotherhood had angered millions of Egyptians.
Mansour held talks on Saturday with the army chief and political leaders, including ElBaradei, on how to pull the country out of crisis as the death toll from Islamist protests over the army's overthrow of Mursi rose to at least 35.
Mansour later summoned ElBaradei back to the presidential palace, the state news agency reported. He was later named prime minister.
A senior official in the Freedom and Justice Party, the Brotherhood's political wing, said he rejected Mohammed ElBaradei's appointment as interim prime minister and described him as Washington's choice.
"We reject this coup and all that results from it, including ElBaradei," Farid Ismail told Reuters at an Islamist gathering in northern Cairo.
Political sources have said ElBaradei, who won the Nobel peace prize for his work as head of the International Atomic Energy Agency (IAEA), would also be acceptable to Western governments that have been reluctant to call the removal of Morsi and his Muslim Brotherhood a military coup.
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