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“We violated our own rule of law by not calling it for what it is because our law clearly states that if it’s a military coup, then aid is cut off. So initially we undercut our own values. … That’s a blow to credibility,” He said on CNN.

Mr. Obama said the U.S. understands the “complexity” of Egyptian politics.

“While Mohammed Morsi was elected president in a democratic election, his government was not inclusive and did not respect the views of all Egyptians. We know that many Egyptians, millions of Egyptians, perhaps even a majority of Egyptians, were calling for a change in course,” the president said.

Mr. Obama said that after the military ousted Mr. Morsi in July, there appeared to be a chance for talks and some sort of reconciliation, but the violence moves the dialogue in the wrong direction.

Analysts said canceling the military exercises was a way of distancing the U.S. from the generals in particular. But the move jeopardizes a key pillar of U.S. military-to-military relations, not just with Egypt but with other allies throughout the region.

“You could argue it’s the centerpiece of the U.S.-Egyptian military relationship,” said Jeffrey White, a former senior defense intelligence official, now a fellow at the Washington Institute for Near East Policy.

“There may be a political case [for the cancellation], but it is not a good thing to do from a national security point of view,” said retired Pentagon analyst and veteran Middle East watcher Michael W.S. Ryan, who used to brief Bright Star participants.

The exercise enables senior officers on both sides to get to know each other and work together, said Mr. White, and “keeping those personal relationships is important, especially in the Middle East.”

The exercise, first staged in 1980, is a fruit of the U.S.-brokered 1979 Camp David Peace Accord between Israel and Egypt. It has been held every two years, but the last Bright Star, scheduled for September 2011, was canceled by mutual agreement because of the upheaval in Egypt at the time, said Max Blumenfeld, a spokesman for U.S. Central Command in Tampa, Fla.

This year’s exercise was scheduled to begin Sept. 18 and was to involve just 2,000 U.S. personnel.

Past exercises have involved paratroop assaults, naval maneuvers and bomb disposal scenarios, and have included forces from Britain, France, Germany, Greece, Italy, Jordan, Kuwait, Pakistan and Turkey.

The Egyptian military co-hosts the exercises on an equal footing with U.S. Central Command, which makes it “an important status symbol” for them, Mr. White said.

There are more practical benefits, Mr. Ryan said. “You want to make sure that the first time you’re cooperating [with allies] isn’t when you have people shooting at you for real,” he said.

He said the exercises had to be staged regularly “because personnel on both sides cycle through [to different jobs] over time, and you lose institutional memory. Plus the threats change,” which means the militaries need to be exercising different capabilities.