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."
Gerges questioned Morsy's ability to continue to lead but said he doubted the military would depose him. Such a move "would plunge Egypt into a greater legal, political and institutional crisis," he said.
The military will want to see the influence of the Muslim Brotherhood reduced in government and in the constitution, Gerges said.
Mubarak had long repressed the Islamic political movement, but it is now the nation's most powerful political force.
Anti-government demonstrators say they have collected 17 million signatures -- 4 million more than the number who voted Morsy into the presidency -- calling for him to go.
The opposition comprises various groups and loose coalitions, some of which are loyal to the ousted Mubarak government, while others want the army to intervene.
AbdulMawgoud Dardery, a former member of parliament and a Muslim Brotherhood representative, told CNN's "Amanpour" that the military could be an "honest broker" in a national dialogue. He said Morsy has reached out to opposition leaders many times, but the opposition "is afraid of democracy."
"It failed in the previous five elections we had in Egypt since the revolution, and they don't want to fail a sixth time," he said. "That's why they're going to street politics."