US Secretary of State Hillary Clinton has voiced support for a "full transition to civilian rule" in Egypt, at the start of a visit to Cairo.
Supporters of new President Mohammed Mursi are in a stand-off with generals who have ruled since President Hosni Mubarak was ousted last year.
Speaking after talks with Mr Mursi, Mrs Clinton said the situation required "compromise and real politics".
She also praised Egypt's military council for its interim leadership.
Mr Mursi, of the Muslim Brotherhood's Freedom and Justice Party, was elected in June in the country's first freely contested leadership vote.
The hour-long meeting between President Mursi and Mrs Clinton was described by a US official as candid and cordial.
Afterwards, Mrs Clinton told reporters: "I have come to Cairo to reaffirm the strong support of the United States for the Egyptian people and their democratic transition.
"We want to be a good partner and we want to support the democracy that has been achieved by the courage and sacrifice of the Egyptian people."
The BBC's Jon Leyne in Cairo says that for all the US fears of an Islamist takeover in recent decades, the governments in Washington and Egypt have now realised they need each other.
Mr Mursi and the Muslim Brotherhood are particularly keen to avoid the sort of international isolation that has been so damaging to other Islamist governments after they have taken office, our correspondent adds.
Saturday's talks launched a series of high-level meetings aimed at stabilising Egypt's fledgling democracy and its alliance with the US.
Mr Mursi has tried to defuse a row over parliament - a body he tried to reinstate by decree last weekend.
The chamber, dominated by Mr Mursi's Islamist allies, was shut down by the military before he took power. The Supreme Constitutional Court has said the dissolution is final.
Mr Mursi says he is "committed to the rulings of Egyptian judges and very keen to manage state powers and prevent any confrontation".
Mrs Clinton said she would meet the head of the Supreme Council of the Armed Forces (Scaf), Field Marshal Mohammed Hussein Tantawi, on Sunday.
He became the country's interim ruler after the fall of President Hosni Mubarak in February last year.
Mrs Clinton praised the role played by the military, but said she would make clear to Field Marshal Tantawi that the US supports the return of the armed forced "to a purely military role".
The secretary of state also encouraged President Mursi to live up to his promises to protect the rights of women and minorities, and to preserve the peace treaty with Israel.
Mrs Clinton arrived in Egypt from a week-long trip to Asia, and will later visit Israel.