CAIRO — Divisions opened Saturday in the mixed coalition of Egyptian activists and politicians who banded together against their country’s Islamist government last week, with a dispute over who would become the interim prime minister showing sharp disagreements about the proper scope of religion in the country’s politics.

Egyptian state media reported — and later rolled back the announcement — that Mohamed ElBaradei, a former chief of the U.N. nuclear agency, had been appointed Egypt’s interim prime minister. The reversal came after Islamists who joined in the coalition against ousted president Mohamed Morsi threatened to withdraw their support if ElBaradei were installed.

“Indications are directed at a certain name, but talks are still ongoing,” said Ahmed el-Moslemany, a spokesman for interim President Adly Mansour, speaking late Saturday at a news conference that had 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. A top aide to ElBaradei had also portrayed the appointment as a done deal Saturday.

But as reports of ElBaradei’s selection filtered out, leaders of the ultraconservative Salafist Nour party threatened to withdraw from the broad coalition of groups backing a path toward elections.

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

Many Islamists view ElBaradei as 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. Mansour also met with representatives from the Nour party and the Tamarod group that organized the protests last weekend that brought millions of people into the streets against Morsi’s rule.

Even before Egypt’s 2011 revolution, ElBaradei — the 2005 winner of the Nobel Peace Prize — had been a harsh critic of former president Hosni Mubarak, who had led the country for three decades.

But ElBaradei’s 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. On Thursday, ElBaradei told CNN he believes Egypt needs a more inclusive government than the one that Morsi and the Muslim Brotherhood had created during their 368 days in power. He said Egypt had risked a “civil war” before the military stepped in to push Morsi out of office.

Although ElBaradei said he wanted a role for members of the Muslim Brotherhood as well as ultraconservative Salafist Muslim groups, he has also defended the shutdown of Islamist television networks, which has deprived Morsi supporters of a platform to broadcast their views domestically in the days since the coup.

More than a dozen top Muslim Brotherhood officials and a lawyer who represents the group remained in detention Saturday, said Heba Morayef, an Egypt researcher for Human Rights Watch.

With Morsi supporters holding firm to demands for his return to the presidency, the discussions over new political leadership took place Saturday as supporters and opponents of the ousted president took stock after a brutal night of clashes. Near Cairo University, a site of conflict between Morsi supporters and security forces in recent days, an encamped group of Morsi backers was reinforcing barricades and preparing for more conflict. At least one man in the crowd fired a gun in the air.

“Everything since Sissi announced the detention of Morsi and the suspension of the constitution has been illegal,” said Medhat Ahmed, a lawyer who had at his feet a plastic bag filled with rocks. “The appointment of this prime minister is illegal and illegitimate in our eyes.”

In Washington, the White House issued a statement Saturday saying that President Obama had convened a meeting of the National Security Council to review the situation in Egypt and that the president “condemned the ongoing violence.” The statement also rejected what it said were claims that the United States is seeking to dictate the course of Egypt’s transition, saying, “The future path of Egypt can only be determined by the Egyptian people.”

Later, Secretary of State John F. Kerry urged a peaceful resolution in Egypt. “At this sensitive moment, we call on all Egyptian leaders to condemn the use of force and prevent further violence among their supporters, and we urge all those demonstrating to do so peacefully,” Kerry said in a statement.

In the early hours of Saturday, Morsi’s Islamist supporters fought brutal street battles with Moris opponents. The violence left at least 30 people dead and more than 1,000 injured across the country, according to Egypt’s Health Ministry.

Also Saturday, a Coptic Christian priest was fatally shot in Egypt’s restive Sinai Peninsula, a local police commander said. Attackers on motorbikes shot the priest, Mena Aboud, in his car in al-Arish, near the border with the Gaza Strip, the commander said. It was not immediately clear whether the killing was connected with Morsi’s ouster.

Abigail Hauslohner, Lara El Gibaly and Amro Hassan contributed to this report.