WASHINGTON—The Obama administration hailed the victory of the Muslim Brotherhood´s presidential candidate in Egypt, Mohammed Morsi, as a key advance for Middle East democracy and a model for other Arab states attempting political transitions.

But beneath the White House´s public pronouncements, fears are mounting inside U.S. national-security agencies about the prospects for Washington´s alliance with Cairo, as well as for the regional interests of the U.S. and its allies.

The White House, while praising the election, cautioned Cairo´s new leader Sunday to respect the rights of non-Muslims and women as he forms a government. It also suggested that Washington expects Egypt´s new Islamist government to maintain and respect the country´s peace treaty with Israel, a cornerstone of the American-Egyptian alliance for the past 30 years.

"We look forward to working together with President-elect Morsi and the government he forms, on the basis of mutual respect, to advance the many shared interests between Egypt and the United States," White House Press Secretary Jay Carney said. "We believe that it is important for President-elect Morsi to take steps at this historic time to advance national unity by reaching out to all parties and constituencies in consultations about the formation of a new government."

President Barack Obama called Mr. Morsi on Sunday, the White House said, adding that Mr. Morsi told Mr. Obama he "welcomed U.S. support for Egypt´s transition."

The White House also said the president called Ahmed Shafiq, who Mr. Morsi defeated, "to commend him on a well-run campaign," adding that he encouraged the general "to continue to play a role in Egyptian politics by supporting the democratic process and working to unify the Egyptian people."

Top diplomats, including the U.S. ambassador in Cairo, have had a number of "friendly contacts" with leading Muslim Brotherhood figures, including the former presidential candidate, Khairat al Shater, and members of the group´s economic team, a senior U.S. official said. In these private talks, Muslim Brotherhood representatives have reassured the U.S. by saying "all the right things on the economic side," the official said, but elements of the group´s social agenda remain a concern for the administration.

"Sure we´ll deal with them. They´re freely elected," the official said.

Depending on how much power the military cedes to the new president, Mr. Morsi´s election potentially could damp U.S.-Egyptian military ties. The U.S. military maintained close relations with its Egyptian counterpart throughout former President Hosni Mubarak´s rule.

In addition to $1.3 billion in annual military aid, U.S. and Egyptian officers held regular exchanges and military exercises to further bind the militaries.

At critical junctures in the transition, Defense Secretary Leon Panetta and other officials have called counterparts in Cairo, urging them to remain committed to elections. A little over a week ago, in a call to Field Marshal Hussein Tantawi, Mr. Panetta pressed the ruling military council to continue with the presidential elections and its democratic transition after a ruling by the country´s high court dissolved Parliament.

In many ways, a Morsi victory was the most desirable outcome for Mr. Obama, who waded deeply into last year´s Arab Spring and had sided against longtime U.S. ally Mr. Mubarak. Still, Mr. Morsi´s win raises numerous challenges to U.S. security interests across the Middle East, said U.S., Arab and Israeli officials

The Muslim Brotherhood´s rise in Cairo is seen as a risk to Israel´s security and a complication to efforts at promoting Arab-Israeli peace talks. Israeli officials in recent weeks have pointed to growing attacks on the Jewish state from the Egyptian-controlled Sinai as evidence that a weakening military in Cairo is less able to secure Israel´s borders and underpin the Israeli-Egyptian peace agreement.U.S. and Arab officials also worry the Muslim Brotherhood´s rise could accelerate the continuing expansion of Islamist governments across the region in the wake of the political uprisings that started last year. Islamist governments have been formed in Libya and Tunisia.

Washington is particularly concerned about the future of Jordan´s King Abdullah, a staunch ally of the U.S. and Israel who has been a key player in combating the role of al Qaeda and Iran in the region. Jordan´s own Muslim Brotherhood movement is driving growing political dissent inside the kingdom.

The U.S. and allied governments also are concerned about developments in Syria, worried that the Brotherhood or a more radical form of Sunni power could gain power as President Bashar al-Assad´s rule weakens.

"It´s scary what the region could look like in a year," said a senior Arab official. "You could have one bloc of the Muslim Brothers and the others close to Iran."

—Adam Entous and Julian E. Barnes contributed to this article. (Copyright © Dow Jones & Company, Inc.) 06/25/12)