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With that in mind, Mr. Danin of the Council on Foreign Relations said the Obama administration risks missing an opportunity to redefine Washington’s relationship with Cairo, which had been warped and misguided during Mr. Mubarak’s reign.

Egypt’s authoritarian era was marked by “an unspoken deal,” in which U.S. leaders would ignore Mr. Mubarak’s autocratic ways as his regime worked toward facilitating U.S. foreign-policy goals in the region, Mr. Danin said.

The overthrow of Mr. Mubarak created “an opportunity to develop and define a new relationship where that’s no longer the bargain,” he said, adding that how Washington conducts itself in response to Mr. Morsi’s power grab will have regional consequences.

“The way in which these issues are sorted out now is very important, not just for Egypt but for the region, especially as others look to Egypt as a critical test of the future and possibilities for real democratic institutions to develop in the Arab world,” Mr. Danin said.

Mr. Shehata said the Obama administration’s plight is complicated by the fact that “the United States is not looked at very favorably by the majority of Egyptians since in the past it was seen as supporting an authoritarian regime.”

As a result, “the United States can’t be seen to be dictating what the Egyptians should create as a democratic system,” he said.

This article is based in part on wire service reports.