For decades under President Hosni Mubarak, the Egyptian military, and the nation’s foreign policy, had been closely allied with the United States and its regional interests. There was concern in Washington after Mr. Mubarak’s ouster that the relationship might not survive — an anxiety that was revived when Mr. Morsi was elected president.

But Washington knew that the longtime defense minister, Field Marshal Mohamed Hussein Tantawi, and his chief of staff, Sami Hafez Anan, still wielded considerable power and were reliable allies.

Then, after an embarrassing terrorist attack in northern Sinai this month, Mr. Morsi appeared to consolidate his power by announcing their replacement, while keeping them on as presidential advisers. The shake-up raised for the first time the possibility that Mr. Morsi might begin to exert some real sway over Egyptian foreign policy, and General Sobhi’s paper suggested that at least some of the younger cadre of generals might share an interest in more independence from Washington.

In his paper, General Sobhi spells out a position that fits well with the campaign vows of many Islamist and secular politicians in Egypt to chart a course more independent of Washington. “If the relationship is between equals, with mutual respect and mutual interest, then nothing changes,” Mahmoud Hussein, the secretary general of the Muslim Brotherhood, said this week of the Egyptian relationship with the United States. “But if the U.S. thinks the relationship with Egypt is of a master and a follower, then this will never be.”

Samer Shehata, a professor of Arab politics at Georgetown University, said American policy makers would be naïve to think that the positions held by Mr. Morsi and the Brotherhood — including criticisms of the United States and strong support for the Palestinians — represented fringe thinking.

On those issues, “the Brotherhood is the Egyptian Kansas,” said Professor Shehata. Their positions on foreign policy “reflect rather than oppose what the Egyptian center is thinking,” he said.

In Washington, officials said they were unconcerned about the paper or the broader changes in the leadership of the Egyptian military. Top United States defense officials have said they enjoy strong and positive relationships with General Sobhi and his boss, the new defense minister, Gen. Abdul Fattah el-Sisi, who also studied at the United States Army War College.