In the face of the anti-government protests, which began over the weekend, five ministers announced their resignations Monday. The latest was Foreign Minister Mohamed Kamel Amr, Egypt's official Middle East News Agency reported.
Demonstrations continued Tuesday in Cairo's Tahrir Square, where thousands of anti-Morsy protesters had massed, cheering as Apache helicopters buzzed the crowd.
The U.S. Embassy in Cairo, which has been closed since June 30, will remain closed on Wednesday.
The UK was warning against all but essential travel to Egypt, and Canada said it was closing its embassy until further notice "for security reasons."
Although the U.S. is urging Morsy to call new elections, it did not say Morsy should step down immediately, the senior Obama administration officials said.
"We are saying to him, 'Figure out a way to go for new elections,'" a senior official said. "That may be the only way that this confrontation can be resolved."
The officials said nothing in the Egyptian constitution gives Morsy the authority to call for new elections but said that may be the only way to end the crisis.
A State Department spokeswoman, however, denied the assertion. "The reports that we have been urging early elections are inaccurate," Jen Psaki told reporters.
The officials said the United States has also warned the Egyptian military that a coup would trigger U.S. legislation that calls for cutting off all American aid.
Psaki acknowledged that "there are conditions on aid," but said, "That's way ahead of where we are in the process."
On Monday, Obama encouraged Morsy in a telephone call to ensure that his government represents all Egyptians, "including the many Egyptians demonstrating."
Morsy's government has insisted that its decisions are legitimate, because it was democratically elected.
Obama addressed this argument directly in his conversation with Morsy.
"He stressed that democracy is about more than elections," the statement said.
Obama reiterated to Morsy that the United States does not support any party or movement in Egypt, it said. He called for an end to violence on all sides and expressed particular concern about sexual assaults on women.
State-funded Egyptian daily Al-Ahram has reported 46 sexual assaults during anti-Morsy protests in Egypt since Sunday, citing the volunteer group Operation Anti-Sexual Harassment.
A Dutch journalist was reportedly raped Friday while covering protests, the Committee to Protect Journalists said. She was hospitalized and underwent surgery before flying back to the Netherlands.
Over the weekend, an Egyptian journalist died in a bomb attack on a Muslim Brotherhood office; four other local journalists were beaten and their camera equipment destroyed or stolen. Two Egyptian journalists were wounded by shotgun fire.
Morsy, a U.S.-educated Islamist, was elected Egypt's president in June 2012, but critics say he has become increasingly authoritarian during his year in power.
And he has failed to revive Egypt's economy, which crashed when the 2011 uprising that toppled Mubarak drove tourists away.
That has disaffected many of his supporters among Egypt's poor and middle classes, said Fawaz Gerges, director of the Middle East Center at the London School of Economics.
"That some of the revolutionaries are calling on the army to return to politics is a testament to how polarized Egypt is a year after the election of Morsy," Gerges said. "Think of the millions of people who cheered Morsy after his election. Think of the millions of Egyptians who pinned their hopes on Morsy.
"A year later, now, the millions of Egyptians who cheered for Morsy are saying he must go."