Aides said both men were updated as increasingly bloody clashes left dozens dead in Egypt, but from outward appearances they gave little sense that the Obama administration viewed the broader crisis in Cairo with great alarm. While the violence distressed American leaders, the unspoken truth is that many of them are at least conflicted and in some cases not all that unhappy about the ouster of President Mohamed Morsi.

The relative calm in Washington also reflects a longer-term shift in American relations in the Middle East. While Egypt was once seen as the singular strategic player in the region, today other countries play a larger role. The overriding American interest in Egypt is preserving its three-decade peace with Israel, which officials believe the military is committed to doing…

Whatever role the administration is playing behind the scenes, its public reticence has suggested its discomfort with choosing sides. In effect, it has accepted Mr. Morsi’s ouster and is not seeking to restore him, reasoning that in fact it could turn out for the best if the military quickly brought about new elections. The main priority is minimizing violence and repression of dissent.

Critics said the administration should have been more outspoken about Mr. Morsi’s mistakes along the way. “They messed up when they did not speak out about Morsi’s undemocratic ways,” said Steven A. Cook, a senior fellow at the Council on Foreign Relations. “It fed a narrative that the U.S. was only interested in stability.”