By Elise Labott
While America's top military officials continue in-depth discussions with their counterparts in Egypt, the Obama administration is looking how to map America's relations with the crucial Middle East ally.
Top officials huddled at the White House again on Monday to discuss the issue.
Defense Secretary Chuck Hagel once again talked with Gen. Abdel Fattah al Sisi, Egypt's defense minister.
It's at least the fourth time Hagel has spoken to Sisi in the past week, both before and after his military deposed Egypt's first democratically elected president, Mohamed Morsy, and put him under house arrest.
Pentagon spokesman George Little said the conversations "have been lengthy and very candid."
A defense official, who requested anonymity, says some of the calls "have lasted nearly two hours."
Meanwhile, Joint Chiefs Chairman Gen. Martin Dempsey has also had two calls with the chief of staff of Egypt's armed forces, Lt. Gen. Sedki Sobhi.
The importance of the U.S.-Egyptian relationship, which has been developing since the Carter-era Camp David Peace Accords, is evidenced by how carefully government officials are avoiding labeling the past week's developments a "military coup."
If Morsy's removal were to be called a coup, under U.S. law, more than $1 billion in military aid to Egypt would have to be slashed.
Israel is concerned that such a cut could jeopardize the peace treaty between the two countries
Israel and Egypt are the two biggest recipients of American military aid.
The determination of whether a coup took place is generally made by the State Department's Legal Advisor Office.
But State Department spokeswoman Jen Psaki described it as an interagency process on Monday.
Psaki also said that the fact tens of millions of Egyptians supported the move and did not consider this a coup would be factored into the deliberations.
Senior U.S. officials say the administration is examining three potential options – calling events in Egypt a coup and cutting off aid; calling it a coup and issuing a national security waiver; or not determining it a coup, recognizing that the military has taken steps to move the country toward a civilian transitional government and move toward elections.
White House spokesman Jay Carney suggested what happens next will be very important.
"Our relationship with Egypt is not limited to or defined solely by the assistance that we provide to Egypt. It is broader and deeper than that, and it is bound up in America's support for the aspirations of the Egyptian people for democracy, for a better economic and political future, and we support that," Carney said.
"So our decisions with regards to the events that have happened recently in Egypt will be - and how we label them and analyze them will be made with our policy objectives in mind, in accordance with the law and in accordance with any consultation with Congress," he said.