In a meeting with Egyptian Foreign Minister Mohamed Amr, Clinton said that the US is not making efforts to arrange such a meeting as it was not appropriate for it to get involved but noted that Washington will support the Middle East peace process.
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Amr, on his part, said that Egypt will honor all the agreements it signed and called for a solution based on a Palestinian capital in Jerusalem.
Earlier, Clinton held her first meeting with Egypt's new Islamist president and said that America's "share strategic interests far outnumber our differences" with Cairo.
Clinton hoped to use the meeting to steer Mohammed Morsi toward opening a dialogue with the military that could end the country's political crisis.
She said afterward that it is up to the Egyptians to decide the way ahead - and that "requires dialogue and compromise, real politics."
Clinton also is voicing support for the democratically elected government and says the US wants to help it be successful.
Clinton's talks with Morsi at the presidential palace kicked off a series of high-level meetings aimed at stabilizing Egypt's democratic transition and its alliance with the United States, once rock-solid but now increasingly shaky. On Sunday, she will meet with Egypt's military chief General Hussein Tantawi.
They didn't shake hands, at least publicly, and their initial greeting was the subject of speculation because of Morsi's Muslim faith.
"Things change (at) kind of warped speed," Clinton told Morsi. The president, speaking in English, said, "We are very very keen to meet you and happy that you are here." Clinton and Morsi were seated perpendicular to one another, the American on a sofa and the Egyptian on a chair.
Clinton is the most senior US official to meet with Morsi, an Islamist who emerged from the country's long-oppressed Muslim Brotherhood movement to be inaugurated as president two weeks ago, after what was regarded as the country's first relatively free and fair presidential election.
Reuters contributed to this report
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