CAIRO—In the months before the military ousted President Mohammed Morsi, Egypt's top generals met regularly with senior aides to opposition leaders, often at the Navy Officers' Club nestled on the Nile.

The message: If the opposition could put enough protesters in the streets, the military would step in—and forcibly remove the president.

"It was a simple question the opposition put to the military," said Ahmed Samih, who is close to several opposition attendees. "Will you be with us again?" The military said it would. Others familiar with the meetings described them similarly.

By June 30, millions of Egyptians took to the streets, calling for Mr. Morsi to go. Three days later, the military unseated him.

Suggestions that Mr. Morsi's overthrow was planned in advance, as opposed to an emergency response, have implications for U.S. aid. "If there was evidence this…was blatantly premeditated, then it would put more pressure to cut off aid on the [Obama] administration, which is currently trying to avoid having to label this a coup d'état," said Josh Stacher, a Kent State University political science professor and Egypt expert.