"I am hopeful that his departure will reopen the path to a better future for Egypt, and I encourage the military and all political parties to cooperate in the peaceful establishment of democratic institutions and new elections that lead to an Egypt where minority rights are protected," said a statement by GOP Rep. Ed Royce of California, who chairs the House Foreign Affairs Committee. "But make no mistake about it, Egypt is in for very difficult days."
A vital U.S. ally
Unrest in Egypt erupted as part of the Arab Spring wave of uprisings that began in North Africa in 2010.
The situation in Egypt has been a political thorn for Obama, forcing him to balance the interests of Israel with a U.S. desire to promote democratic values in the mostly Islamic region.
Before Morsy's election, Obama announced efforts to help Egypt stabilize and modernize its economy, including debt relief of up to $1 billion and another $1 billion in loan guarantees.
Morsy's ascendency benefited Obama a few months later, when Morsy played a key role in negotiating a cease-fire between Hamas and Israel following eight days of Gaza violence last November.
But Morsy subsequently issued an order preventing any Egyptian court from overturning his decisions in what was considered an undemocratic move decried by opposition groups.
Within a month, he reinstated the judicial oversight and submitted a draft Islamist-backed constitution that voters approved and he signed into law.
Public anger over economic woes and a lack of opposition voices in government helped spark the latest protests.
Obama had called Morsy
The White House said on Tuesday that Obama had called Morsy to urge him to show Egyptians that he understood their anger and to take political steps to resolve the crisis.
The focus and tone of the White House statement was similar to a year ago when Morsy won Egypt's first election following Mubarak's ouster.
"We will stand with the Egyptian people as they pursue their aspirations for democracy, dignity, and opportunity, and fulfill the promise of their revolution," the White House said then.
Such a neutral approach has riled conservatives seeking a more assertive U.S. role in the aftermath of the Arab Spring uprisings that swept through parts of North Africa and the Middle East in recent years.
Republican Sen. John McCain of Arizona has criticized the president for yielding a leadership role in the region.
Shrinking U.S. aid
Last month, he warned a shrinking U.S. foreign aid budget meant "Egypt must show that it is a good investment of our scarce resources -- that the return on this investment will be a freer, more democratic, more tolerant Egypt."
If not, McCain said in a speech on the Middle East, "Congress will spend this money elsewhere. That is just a fact."
The Egyptian military this week gave Morsy an ultimatum to work out a solution to the protests by Wednesday. Morsy responded by calling for creation of a temporary coalition government until early elections can take place in coming months.
The statement posted Wednesday on Morsy's official Facebook page warned that a coup would undermine the aspirations and achievements of the 2011 revolution.
Travel warning, evacuation
The U.S. Embassy in Cairo ordered the mandatory evacuation of all nonessential personnel, CNN's Jill Dougherty reported, citing a senior administration official.
Separately, the State Department warned Americans to defer travel to Egypt and U.S. citizens living there to leave the country.