Two American officials said the U.S. government would prefer that Mubarak, 82, not run for re-election in presidential voting scheduled for September.
The officials spoke on condition of anonymity because of the sensitivity of diplomacy and the difficult situation the Obama administration finds itself in.
Washington is trying to smooth the way for a more representative government in Egypt without alienating pro-democracy protesters or its ally over three decades.
The U.S. is pressing Mubarak to institute a set of reforms as a first step toward meeting the demands of protesters clamoring for his ouster. The immediate gestures are for Mubarak to lift emergency laws in place since 1981, allow non-governmental organizations to operate and free political prisoners.
Open, fair elections are the fourth and perhaps most important thing Washington is urging on Mubarak.
The U.S. cannot force him to accept any of those conditions, although it has leverage born of 30 years of partnership and billions in aid.
American officials continued to wrestle with the dilemma Monday of strengthening support for peaceful demonstrations, while not completely undercutting Mubarak, whose close cooperation with the United States on Israeli-Arab peace talks and other issues has made Egypt America's most important ally in the Arab world.
A coalition of opposition groups hasto take to Cairo's streets Tuesday to demand Mubarak's removal.
In an apparent attempt to defuse the weeklong political upheaval, Mubarak named a new government Monday, but the appointments were treated with scorn by demonstrators.
The United States, too, is unsatisfied with the response so far from Mubarak, officials said.
President Obama called last week for "concrete steps" to expand rights, but avoided outlining the specific steps expected of Mubarak.
White House Press Secretary Robert Gibbs said Monday that it was, "not for
me or our government to determine" whether Mubarak should leave office.
Gibbs said the U.S. was "not picking between those on the street and those in the government." Yet he also said the U.S. was seeking an "orderly transition" in Egypt.
Asked what he meant with those words, the press secretary said the United States wanted to see, "a process of negotiations with a broad cross-section of the Egyptian people, including those that are in the political opposition at the moment."
He again emphasized the administration's official neutrality: "That's not for us to determine what the parameters and what the limits of those (changes) are... But undoubtedly transition in this case means change. There's no doubt about that."
Part of the hesitancy is that the U.S. doesn't want to give the impression that its backing for Mubarak is dependent on a small list of reforms.
Otherwise, a new dilemma could arise. If the Egyptian government meets U.S. expectations, does the Obama administration congratulate Mubarak and risk undercutting Egyptian democracy activists? Or, does it continue to press for greater reforms, potentially alienating an ally even while it is showing signs of becoming a democracy.
The U.S. would likely have to respond to genuine reforms in Egypt with a delicate combination of support for pro-democracy reforms as they are instituted, and calls for continued action.
Beginning less than two weeks after Tunisian protesters ousted their long-time president, the Egyptian unrest has had the United States in a bind since its start. The U.S. has spent billions establishing Egypt as a bulwark of American influence in the Middle East and the government's collapse could threaten efforts from an Israeli-Palestinian peace deal to counterterrorism operations and pressure on Iran.
Secretary of State Hillary Rodham Clinton appealed Sunday for an orderly transition to lasting democracy in Egypt and said U.S. officials "obviously want to see people who are truly committed to democracy, not to imposing any ideology on Egyptians."
She warned Sunday against a takeover resembling the one in Iran three decades ago, with a "small group that doesn't represent the full diversity of Egyptian society" seizing control and imposing its ideological beliefs.
The unspoken concern is that an Egyptian revolution could make American foreign policy dramatically more difficult in the Middle East.
The State Department said more than 220 Americans have left Egypt on special flights out of the country, including dozens who got on a military plane that was already in the country and had available seats. More flights are scheduled.
The department said itabout 900 U.S. citizens from Egypt on Monday and another 1,000 on Tuesday.