CAIRO — Egypt’s new leaders struggled to put together a new government on Saturday, with disagreements over who should be the interim prime minister spilling out into public view and showcasing the divisions among those who had endorsed the overthrow of the country’s first democratically elected president.

State news media initially reported that Mohamed ElBaradei, the Nobel Prize-winning diplomat and a vocal critic of Egypt’s last three leaders, had been chosen as prime minister, a move that would have given the generals who ousted President Mohamed Morsi a head of government likely to appeal to the country’s liberals and to the West.

But within hours, the fissures that had vexed Mr. Morsi’s rule re-emerged to undo the reported decision. The ultraconservative party Al Nour, the one Islamic faction that had backed the military takeover, said it would refuse to work with Mr. ElBaradei because of his liberal views. Around midnight, after hours of contradictory news coverage, the new interim president then backed away from the earlier reports that Mr. ElBaradei had been offered the job.

The continued chaos underlined the struggle for stability in Egypt, which has lurched from crisis to crisis since the Arab Spring revolution that overthrew President Hosni Mubarak in 2011. Since then, Islamists and liberals have battled for power, even after Mr. Morsi and the once-banned Muslim Brotherhood won multiple rounds of elections.