After the talks, Hillary Clinton reaffirmed Washington’s support for a “full transition to civilian rule” in Egypt.
President Mohammed Mursi has become embroiled in a constitutional crisis after trying to reinstate a parliament dissolved by the judiciary and the military.
Hillary Clinton has backed Mohammed Mursi, saying Egyptians should get the government they voted for.
Mohammed Mursi, of the Muslim Brotherhood’s Freedom and Justice Party, was elected in June in the country’s first ever freely contested leadership vote.
After the meeting in Cairo, Hillary 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.”
Not many years ago, one US secretary of state declared that Washington did not speak with the Muslim Brotherhood, and never would.
But the administration of Barack Obama has been quick to engage with the new president – a case of accepting the inevitable and trying to make the best of it.
The US government wants to see Egyptian democracy and human rights being protected.
The Muslim Brotherhood has repeatedly stressed it does not want to be isolated internationally, not least because the country depends so heavily on international trade and tourism.
Mohammed Mursi has tried to defuse the row over parliament – a body he tried to reinstate by decree last weekend.
The chamber was dominated by Mohammed Mursi’s Islamist allies, and was shut down by the military before he took power.
The Supreme Constitutional Court has said the dissolution is final.
Mohammed Mursi has said he is “committed to the rulings of Egyptian judges and very keen to manage state powers and prevent any confrontation”.
Hillary 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.
Asked what she would tell Field Marshal Tantawi, Hillary Clinton said she would make clear the US supports the return of the armed forced “to a purely military role”.
Earlier this week, Hillary Clinton said Egyptians should “get what they protested for and what they voted for, which is a fully-elected government making the decisions for the country going forward”.
Hillary Clinton arrived in Egypt from a week-long trip to Asia, and will later visit Israel.
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