CAIRO—Divisions opened Saturday in the mixed coalition of Egyptian activists and politicians who banded together against their country’s Islamist government this week as a dispute arose over who would become the interim prime minister.

Egyptian state media reported that Mohamed ElBaradei, a former chief of the UN nuclear agency, had been appointed the interim prime minister. A top aide to ElBaradei also portrayed the appointment as a done deal. Then just hours later the announcement was rolled back.

The sudden reversal came after Islamists who had joined in the coalition against ousted president Mohammed Morsi threatened to withdraw their support if ElBaradei were installed.

“Indications are directed at a certain name, but talks are still ongoing,” Ahmed el-Moslemany, a spokesman for interim President Adly Mansour, said late Saturday at a news conference that had earlier been billed as an announcement of a new prime minister.

The unusual back-and-forth suggested that ElBaradei — a divisive figure in Egypt who is seen as a staunch secularist by groups who want a greater role for religion in politics — may have proved too controversial a choice as prime minister.

But as reports of ElBaradei’s selection filtered out, leaders of the ultraconservative Nour party, the second leading religious party after the Muslim Brotherhood, threatened to withdraw from the broad coalition of groups backing a path toward fresh elections.

“The nomination of ElBaradei violates the road map that the political and national powers had agreed on with Gen. Abdel Fatah al-Sissi,” Ahmed Khalil, the Nour party’s deputy leader, told the state-run Al-Ahram newspaper.

Many Islamists view ElBaradei — the 2005 winner of the Nobel Peace Prize — as a leader who is uninterested in giving them a say in Egypt’s affairs.

“Baradei in a way is kind of the ultimate liberal,” said Shadi Hamid, an Egypt expert at the Brookings Doha Center. “He has a very antagonistic relationship with the Muslim Brotherhood, which is why it doesn’t bode well for Brotherhood reintegration (if he were to come to power).”

Just as the democratically elected Morsi experienced a remarkable fall from grace this week, ElBaradei’s unelected rise to the position of prime minister would have marked a remarkable turnaround for a politician who has struggled to find popular support outside Egypt’s urban, educated classes, in a country where roughly half the population lives on less than $2 a day.

Before the announcement of ElBaradei was reversed, state television broadcast images of him meeting with Mansour at the presidential palace. It was the first time Mansour had worked from the palace since he took office Thursday, hours after Wednesday evening’s coup.

Even before Egypt’s 2011 revolution, ElBaradei had been a harsh critic of former president Hosni Mubarak, who had led the country for three decades.

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But his long career outside Egypt, first as a diplomat with Egypt’s Foreign Ministry and then at the International Atomic Energy Agency in Vienna, led critics in Egypt to say he was more recognizable abroad than at home. He was director general of the nuclear watchdog from 1997 until 2009. Upon returning to Egypt, he spoke out against Mubarak and worked with others, including the then-banned Muslim Brotherhood, to campaign against the leader.

That alliance withered after the 2011 revolution.

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