While Mr. Morsi served as head of state, Israel’s only line of communication with Cairo was through the Egyptian military and security establishment, which is now controlling Egypt’s political process. Perhaps more reassuring to Israel is the role of Gen. Abdul-Fattah el-Sisi, the top commander who led the move to depose Mr. Morsi.

General Sisi is well known in Israel’s defense establishment from his past roles in military intelligence and in northern Sinai. An Israeli expert said that even after Mr. Morsi appointed General Sisi as his defense minister, the general’s office continued to communicate and coordinate directly with Israel.

Israeli officials have maintained a diplomatic silence since Mr. Morsi’s overthrow, refusing to comment publicly on what they say is an internal Egyptian affair.

“We are observing very closely,” one official said, speaking on the condition of anonymity because he was not authorized to discuss the issue publicly. “This is a matter of highest importance for us. We really hope the Egyptians manage to put together a functioning democracy, slowly but surely, but there is still a very high level of uncertainty.”