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The delay triggered protests by Morsi supporters who suspected that the military was trying to steal their candidate’s victory.

“There really wasn’t a question of whether the results were in dispute. The question was what are the rules of the road going forward between the Brotherhood, President Morsi and the military,” said Mr. Cook, author of “The Struggle for Egypt.” “Clearly, some sort of deal has been struck.”

Earlier this month, Egypt’s Supreme Constitutional Court ruled that the Islamist-dominated parliament must be dissolved because a third of its members had been elected illegally.

In a separate decision, the court rejected a law enacted by the parliament that prohibited former senior members of the Mubarak regime from running for office. That ruling paved the way for Mr. Shafiq to challenge Mr. Morsi.

In addition, the military gave itself powers that curbed the president’s authority and put the generals in charge of overseeing the writing of Egypt’s new constitution.

It also reinstated an emergency law that expanded police powers and suspended constitutional rights.

Analysts interpreted these moves as an attempt by the military to hedge against a Morsi victory, and State Department spokeswoman Victoria Nuland said last week that they “appear to prolong the military’s hold on power.”

On Sunday, Mr. Carney commended the military for supporting “a free and fair election.”

Dave Boyer contributed to this report.