Since Mr. Morsi was deposed, the killing of security officers has become an almost daily occurrence in the industrial canal zone of the lawless northern Sinai. But the car bomb on Monday morning in the south Sinai town of El Tur, in the same region as the biblical Mount Sinai and the Sharm el Sheik resort, was the first sign that such attacks might be spreading to what had been a pillar of the Egyptian economy, its Red Sea resorts.

And the rocket-propelled grenade attack was the first time in years that such a heavy weapon had been used in the vicinity of the capital. The grenade tore a foot-wide hole in a satellite-transmission dish, and its explosion an hour before dawn sent shivers through the affluent neighborhood of Maadi, a heavily guarded precinct that is home to many embassies and diplomats.

No one claimed responsibility for the attacks, nor did they need to. The attacks were universally assumed to be the work of Islamists angry at Mr. Morsi’s ouster, and, speaking on the condition of anonymity because they were not authorized as spokesmen, two senior government officials blamed the Brotherhood despite its repeated public disavowals of such tactics.

“Blackmail by terrorism,” said one of the officials, a senior military officer.

Suggesting the Brotherhood was almost predisposed to violence, he argued that the violence might have been worse if not for the crackdown, in which security forces have killed more than 1,000 protesters and jailed hundreds of Islamist leaders. If the violence was this severe with the leaders behind bars, the officer asked, how much worse might it be if leaders were released?

The Brotherhood’s “anti coup” alliance, meanwhile, saluted what it called the courage and sacrifice of “unprecedented numbers” who had turned out the day before. In a statement on Monday, the alliance called for student protests at schools and universities on Tuesday “to denounce the continuation of the massacres.”

And it all but dared the government to continue the violence against protesters by calling for new marches on Friday to Tahrir Square, the symbolic center of the 2011 revolt against President Hosni Mubarak and more recently the staging ground for rallies in support of General Sisi. It was the attempt by pro-Morsi marchers to reach Tahrir Square on Sunday, when it was the site of a pro-military celebration, that set in motion the day of deadly violence, and the opposition alliance’s plans to try again this Friday appeared to set the stage for more.