Khairat el-Shater, the deputy chief of the Muslim Brotherhood who has been detained by the Egyptian government, was visited by U.S. Deputy Secretary of State William J. Burns on Sunday. (2012 photo by Nariman El-Mofty/AP)

The Obama administration sought to defuse tensions with the interim Egyptian government and the Muslim Brotherhood on Monday, deploying a senior diplomat to quietly press the case that street protests and political deadlock will not return Mohamed Morsi to the presidency.

Deputy Secretary of State William J. Burns, together with envoys from the European Union and two key Arab nations, met late Sunday with the detained deputy chief of the Muslim Brotherhood. But U.S. officials said separately that one of Burns’s goals has been to smooth relations with Egypt’s military-backed interim government and make clear that the United States is distancing itself from Morsi.

The message is being delivered as nearly every faction in Egypt expresses anger with the U.S. response to the country’s constitutional crisis, which is stretching into a second month. Egypt’s powerful army chief has accused Washington of abandoning the country.

“You left the Egyptians. You turned your back on the Egyptians, and they won’t forget that,” Gen. Abdel Fatah al-Sissi said in a Washington Post interview published over the weekend. “Now you want to continue turning your backs on Egyptians?”

The White House has refused to call the military’s ouster of Morsi a coup, because doing so would automatically bar the United States from dispensing more than $1 billion in annual aid to Egypt. The money represents much of the leverage that Washington holds over a key Middle East partner that was the first Arab state to make peace with Israel.

At the same time, weeks of muddled messages have left Egypt’s interim government angry and dissatisfied.

U.S. officials said they are urging calm among all factions in Egypt. “We all are encouraging the Egyptians to be part of an inclusive process that includes the Muslim Brotherhood,” State Department spokeswoman Marie Harf said Monday.

Two Republican senators who are frequent critics of the Obama administration on foreign policy — John McCain (Ariz.) and Lindsey O. Graham (S.C.) — have traveled to Egypt to reinforce the U.S. view that it must move more quickly and clearly toward a new elected government.

Burns, meanwhile, has extended his stay in Cairo after arriving Friday. U.S. officials said Egypt’s government cooperated in arranging his meeting with Khairat el-Shater, the jailed deputy chief of the Muslim Brotherhood.

The State Department would not comment on whether Burns proposed a bargain to release jailed Brotherhood figures in exchange for an end to street protests and encampments by the movement’s supporters. There are no plans for Burns to see Morsi in jail, Harf said, but she brushed aside suggestions that by not seeking a meeting with Morsi the United States is making its preference clear.

“We’re not taking a side. We’re not taking a party. And he’s making that point to everybody,” she said.

More privately, U.S. diplomats are underscoring the notion that the United States has moved on and that Morsi’s supporters should, too, according to officials, who spoke on the condition of anonymity to discuss sensitive diplomacy.

Secretary of State John F. Kerry has presaged that message in a subtle way, putting distance between the United States and Morsi, whose tilt toward authoritarian rule since last fall had deeply worried his already skeptical U.S. backers.

“Egypt needs to get back to a new normal. It needs to begin to restore stability to be able to attract business and good people to work,” Kerry said in London on Friday.

The top U.S. diplomat said he was clarifying remarks from a day earlier, in a TV interview, that were interpreted as an endorsement of the Egyptian military’s ouster of Morsi.

Speaking to Pakistan TV, Kerry had said that the interim Egyptian government was “restoring democracy.” He added caveats about the need for a quick transition to elected rule in Egypt but said he did not think the military had taken over the country. The remarks were criticized by the Muslim Brotherhood and by Turkey, whose help Kerry has sought to resolve the Egypt crisis.

Kerry spoke before a meeting with Sheik Abdullah bin Zayed, the foreign minister of the United Arab Emirates, whose government is in close contact with the Egyptian military and interim government. Separately, Kerry and other U.S. officials have sought help from the Persian Gulf state of Qatar, which has close ties to the Muslim Brotherhood. Envoys from both nations joined Burns for the meeting Sunday with Shater.

Kerry spoke to Qatari Foreign Minister Khalid bin Mohammad al-Attiyah on Friday, their seventh conversation since July 26, according to a senior State Department official who spoke on the condition of anonymity to detail the sensitive diplomacy.

That was more calls than took place between Kerry and any other single player in the same period amid the international diplomacy concerning Egypt. Kerry had six conversations with Mohamed ElBaradei, Egypt’s interim vice president, and two with the nation’s foreign minister.

Kerry has said nothing about Morsi’s fate, which is unclear. Morsi was never popular with U.S. officials. A severe figure and unapologetic Islamist despite a formal departure from the Brotherhood upon election last year, he made little attempt to court the Americans.

Morsi gained credibility in Washington late last year by helping broker a cease-fire between Israel and Palestinian militants in the Gaza Strip, but he quickly lost it through a series of increasingly authoritarian moves. An unwillingness or inability to grapple with crippling economic problems further alienated him from Egypt’s largest donor.

Burns’s meeting with Shater came nearly a week after the European Union’s foreign policy chief, Catherine Ashton, was granted a meeting with Morsi. Ashton said Morsi told her that he remains the legitimate elected president, suggesting that he would reject a deal that released him from jail but did not restore him to office.

Shater, a businessman who serves as deputy to the Brotherhood’s leader, has been accused of complicity and incitement in the killing of eight demonstrators outside the organization’s Cairo headquarters. Before his arrest, he was widely seen as one of the real powers behind the Morsi presidency.