Mr ElBaradei's nomination had been confirmed by state media on Saturday, but the U-turn came amid opposition to the appointment by the Nour Party, Egypt's second Islamist force.
ElBaradei PM appointment in doubt as Islamists call more protests
CAIRO // Egypt's political transition after President Mohamed Morsi was ousted by the military stumbled at the first hurdle, after the choice of liberal politician Mohamed ElBaradei as interim prime minister was thrown into doubt by Islamist objections.
Mr ElBaradei's nomination had been confirmed by several sources and state media on Saturday, but just before midnight a presidential spokesman told reporters that the prime minister had not in fact been chosen.
The abrupt U-turn came amid opposition to the appointment by the Nour Party, Egypt's second Islamist force after Mr Morsi's Muslim Brotherhood movement, highlighting the challenge the military faces in finding consensus among liberals and conservatives on who should run the country.
Clashes between tens of thousands of pro- and anti-Mursi protesters swept the Arab world's most populous nation on Friday and at least 35 people were killed and more than 1,000 wounded.
The violence, which saw rival factions fighting street battles in central Cairo and many others cities and towns, underlined the pressing need for a swift political solution seen as inclusive to all.
"We extend our hand to everyone, everyone is a part of this nation," the spokesman said. "The Muslim Brotherhood has plenty of opportunities to run for all elections including the coming presidential elections or the ones to follow."
Minutes after he spoke, state media reported that the public prosecutor ordered that four top Brotherhood leaders held this week be detained for a further 15 days on accusations that they incited violence against protesters.
The four included Saad El Katatni, head of the group's political wing, and Khairat El Shater, its political strategist.
The Brotherhood has said it wants nothing to do with the military's plans for a new interim government. It believes Mr Morsi should be reinstated, and has pledged to keep protesting until he is.
The Nour Party, however, had agreed to the army-backed transition plan leading to new elections. Its withdrawal from the process would strip that plan of vital Islamist support.
And following the Nour rejection, the interim administration headed by Adly Mansour delayed naming the new prime minister.
On Sunday, eople were still reeling from one of the bloodiest days in over two years of tumultuous upheaval since autocrat Hosni Mubarak, who ruled for 30 years, was toppled in a popular uprising that was part of the 2011 "Arab Spring".
The Brotherhood called for another day of protest on Sunday, meaning that relative calm on Saturday may prove to be only a temporary lull.
Huge protests were staged on June 30 to pressure Mr Morsi into resigning amid growing anger at economic stagnation and the perception among many that the Brotherhood was seeking to take control of every part of the state - a charge it fiercely denies.
Millions took to the streets to cheer his removal on Wednesday, but for many Islamists it was a bitter reversal that raised fears of a return to the suppression they endured for decades under autocratic rulers.
The military said it had not carried out a coup, but merely enforced the will of the people.