“We are taking the heat from both sides,” Gehad el-Haddad, a spokesman for the Brotherhood, acknowledged Thursday as the group responded belatedly with a televised presidential address, a letter to the editor in The New York Times by its top strategist, and a series of sympathetic online messages aimed at mollifying American officials.

After decades focused on disciplining its own cadre to survive underground, the Brotherhood’s leadership is still adjusting to the competing constituencies and high visibility of democratic life.

“They realized a little after the fact the degree of fallout in the U.S. and that is why you are seeing all these conciliatory statements from Brotherhood leaders today,” said Shadi Hamid, director of research at the Brookings Doha Center, who follows the group closely. “Morsi is doing a difficult dance.”

Evidently paralyzed by the conflicting pressure, Mr. Morsi had remained conspicuously silent as protesters breached the walls of the American Embassy in Cairo — a stark contrast to the help, contrition and condemnation coming from the new government of Libya , where gunmen set fire to an American diplomatic mission in Benghazi, killing Ambassador J. Christopher Stevens and three other Americans.

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On Wednesday, Mr. Obama, who is campaigning, called staff members at the White House from Air Force One to arrange a telephone call to Mr. Morsi, a senior administration official said.

The president was not happy; Egypt, unlike Libya, is crucial to American security interests, given its peace treaty with Israel . At 11 p.m., from his hotel suite in Denver, Colo., Mr. Obama got on the phone with Mr. Morsi, who began by offering condolences on the American deaths in Libya.

But that was not what Mr. Obama was calling about.

“The president made his point that we’ve been committed to the process of change in Egypt, and we want to continue to build a relationship with the Egyptian government,” said a senior administration official. “But he made it clear how important it is that the Egyptian government work with us to lower the tension both in terms of the practical cooperation they give us and the statements they make.”

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Mr. Morsi brought up the American-made video attacking the Prophet Muhammad, which had set off the violent protests, and Mr. Obama said he understood the ire felt by Muslims, but added that it did not justify attacks on the embassy.

Mr. Obama urged Mr. Morsi to publicly and strongly condemn the attacks. He had already signaled his displeasure earlier, saying in an interview on Telemundo that Egypt was not necessarily an “ally,” although White House officials were playing down the remark on Thursday.

“ ‘Ally’ is a legal term of art,” said Tommy Vietor, a spokesman with the National Security Council . “We don’t have a mutual defense treaty with Egypt like we do with our NATO allies.”

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The pressure from Mr. Obama put Mr. Morsi in a vise grip of competing values and world views. Scholars say the furor here reflects different traditions when it comes to religious rights and freedoms. Where Americans prize individual choice, Egyptians put a greater emphasis on the rights of communities, families and religious groups. On the third day of increasingly violent protests outside the American Embassy, many demonstrators said their main demands were directed at Mr. Morsi, insisting that he needed to be firmer with the United States if it failed to punish the filmmakers.

“Morsi needs to take firm action,” said Hesham Nawar, 25, clutching two spent canisters of tear gas and blaming the president for the clashes. Islamist politicians, he said, “rise up and mobilize millions for politics, but they do not come out for the prophet now.”

But the war of words was continuing in Cairo on Thursday.

The United States Embassy publicly mocked the Brotherhood for sending out conflicting messages in its English and Arabic Twitter accounts. “Egyptians rise up to support Muhammad in front of the American Embassy. Sept. 11,” read an Arabic language post the Brotherhood sent out on the day of the attacks — one of several over the last few days emphasizing outrage at the video or calls for its censorship.

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So on Thursday, when the group sent out a message of sympathy and support from its top strategist, Khairat el-Shater , from its English-language Twitter account, the Embassy responded tartly via Twitter. “Thanks,” its message read, “By the way, have you checked out your own Arabic feeds? I hope you know we read those too.”

By midday, searching for a middle ground, Mr. Morsi appeared on national television, telling Egyptians it was their “religious duty to protect our guests and those who come to us from outside our nation,” including their embassies, and businesses. “I know that the people attacking the embassies do not represent any of us. We all have to cooperate to express opinions while maintaining our principles, our correct peaceful ways that the whole world accepts,” he said.

Mr. Morsi offered condolences for the American ambassador killed in Libya, in a parallel protest over the same video, and he vowed to bring charges against those who had scaled the embassy walls in Cairo. At the same time, however, he was also careful to stress the legitimacy of the protesters’ grievances. “We all reject any trespassing or offense to our Prophet Muhammad,” Mr. Morsi said, adding, “We oppose anyone who offends our prophet with words, actions, expression. This is rejected by all Muslims and all Egyptians.”

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Mr. Haddad, the Brotherhood spokesman, defended the Brotherhood’s attempt to modulate its messages to the Egyptian streets and the Western world.

“Speaking to the angry Muslims of Egypt, we told them we understand your anger, you are right to be angry and we share it — but let’s all express our anger in the right way and control it. And on the other side we tell the international world that we condemn these attacks and we urge restraint,” he said. Both messages were consistent, he said, and sought to preserve enough trust to resolve the tension.

In the letter to The Times, Mr. Shater, the Brotherhood strategist, said: “Despite our resentment of the continued appearance of productions like the anti-Muslim film that led to the current violence, we do not hold the American government or its citizens responsible for acts of the few that abuse the laws protecting freedom of expression.”

For Mr. Obama, the fear is that Egypt’s initially tepid reaction to the attacks could set a dangerous precedent, as the administration tries to find its footing with the populist governments that emerged from the Arab uprisings. Any estrangement with Egypt could bleed into Cairo’s relationship with Israel — a cold peace since the two countries signed a treaty at Camp David more than 30 years ago.

Mr. Obama’s impatience with Mr. Morsi stems in part from the administration’s belief that the United States eventually threw its weight behind the democracy movement in Tahrir Square last year, and has continued to back the Arab street, at least in Egypt.

But it is perhaps the 30-year long alliance with the Egyptian military, and Mr. Mubarak, that is still on the minds of many joining anti-American protests, foreign policy experts suggest.

“Part of what we’re seeing is the residue of support for 30 years of the Mubarak dictatorship, and that has never been decisively confronted by American officials,” said Tom Malinowski, of Human Rights Watch . “There’s also all the old anger of the Israeli-Palestinian issue, and the sense among some that U.S. support for the Tahrir Square movement came a few days, or even a few hours, too late for their taste.”