Mr. Morsi insisted he was not ignoring the court, but merely setting a time frame for carrying out its decision. His office fired back with a robust defense of his order, saying a provision that called for the election of a new Parliament showed his respect for the court’s rulings. Hours later, the military issued a statement justifying its power grab by saying it was imposed by “necessity and the political, judicial and constitutional circumstances the country is going through.”

The brinkmanship and the profusion of legal arguments clouded a subtler duel between the Brotherhood and the military. In many ways the court and the president are proxies for a fight between the nation’s oldest and most influential Islamist organization and appointees of the ousted president, Hosni Mubarak. In Egypt’s postrevolt politics, their ideological struggle has been eclipsed by a more fundamental conflict, between “elected and unelected parts of the state,” Professor Ghobashy said.

During its decades as Mr. Mubarak’s principal opposition, the Brotherhood was officially banned but allowed to operate, with its leaders frequently jailed to further keep the organization in line. Professor Ghobashy said that although the military realized that the “Mubarak model” was no longer an option, “they want to figure out some stable way to allow” the Brotherhood into power.

The two groups, Professor Ghobashy said, were engaged in “a competitive dance.”

“They’re working out what the long-term settlement will be,” she said. “Egyptian politics is a contest for what the new ruling formula will look like.”

In that context, each group has clung stubbornly to its priorities. Mr. Morsi cannot succeed without Parliament, which he needs to broaden his legitimacy by passing popular laws and helping advance his agenda. The military has focused on the Constitution, demanding that it be allowed to challenge provisions it does not like, especially those that potentially curb the military’s power.

While there was little evidence that the two sides were engaged in any direct negotiation, the power struggle that has upended Egyptian politics seems to reflect the groups’ attempts to reach some sort of accommodation, as they have historically.