Mr. Obama’s statement, the senior administration official said on Wednesday, was calculated to give the Egyptian military a window to stabilize the country. But if it used the takeover as a pretext to further crack down on Mr. Morsi or the Muslim Brotherhood, he said, the president would use harsher words and raise the threat of cutting off aid.

The United States provides $1.3 billion a year in military aid to Egypt, making it the second-largest recipient of American foreign assistance, after Israel. However, the military’s actions could put that at risk, said the chairman of the Joint Chiefs of Staff, Gen. Martin E. Dempsey.

“If this were to be seen as a coup, then it would limit our ability to have the kind of relationship we think we need with the Egyptian armed forces,” General Dempsey said in an interview that was taped Wednesday to be aired Sunday on “State of the Union” on CNN.