WASHINGTON—The Obama administration increasingly fears that Egypt's military, ignoring American appeals, is deepening a crackdown that could spark a sustained period of instability and lead members of the country's Muslim Brotherhood to take up arms.

In a series of private messages in recent days, Defense Secretary Chuck Hagel and other American officials warned Egyptian military leader Gen. Abdel Fattah Al Sisi that his clampdown on the Brotherhood risked driving the Islamist group back underground, say U.S. officials involved in the discussions.

Despite those exhortations, Gen. Sisi called for massive demonstrations on Friday, which precipitated the deadliest single incident in the more than two years since Egypt's revolution. The U.S. also had sent messages urging calm to Brotherhood leaders, but officials said the group, like the military, showed little sign of backing down.

At least 74 people were killed and hundreds of others were injured early Saturday when security forces fired live ammunition on Brotherhood backers during chaotic counter-demonstrations by both sides.

On Sunday, the scene in Cairo was mostly calm and Western diplomats expressed hope that a European Union delegation, led by foreign policy chief Catherine Ashton, would be allowed to visit with former President Mohammed Morsi on Monday. Such a visit, the first since Mr. Morsi's arrest, could be a sign that Gen. Sisi may be trying to lower the temperature and respond to American and international demands, U.S. officials said.