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By Arshad Mohammed
CAIRO, July 14 (Reuters) - Hundreds of people chanted anti-U.S. and anti-Islamist slogans outside Hillary Clinton's hotel on Saturday as the U.S. secretary of state urged Egypt's military and Muslim Brotherhood to complete a transition to full democratic rule.
Clinton met Egypt's newly-elected Islamist President Mohamed Mursi on Saturday and was to see military chief Field Marshall Hussein Tantawi on Sunday, two of the central players in the power struggle playing out in the country.
After a more than one-hour meeting with Mursi, Clinton made clear Washington wants Egypt's political players to reach some consensus that would lead to genuine democracy, with the military returning to a purely national security role.
But she stressed it was up to the Egyptians themselves to decide how to achieve this, sorting out such questions as what kind of a constitution to draft and when and whether to hold new parliamentary elections.
"Democracy is hard," Clinton told a news conference with Egyptian Foreign Minister Mohamed Kamel Amr. "It requires dialogue and compromise and real politics."
"GET OUT HILLARY"
Clinton got a taste of democracy in action when protesters, most of them backers of the old regime of former President Hosni Mubarak, a long-time U.S. ally toppled by popular protests last year, demonstrated outside her five star hotel.
"Get out Hillary," they chanted. "We don't want the Muslim Brotherhood."
Among the signs held up were "America: Support Liberty Not Theocracy" and "Egypt Majority is not Islamist."
Clinton is the most senior U.S. official to meet Mursi, 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.
The army, in power for six decades, moved to limit the power of the new civilian president even as voters were lining up to elect him.
During last month's two-day run-off election, generals dissolved parliament and issued a decree restricting the president's powers. Mursi quickly asserted his own authority, issuing a decree summoning the disbanded, Islamist-led parliament just days after he took office.
The lawmakers met on Tuesday. Judges, seen as allies of the generals, responded by rebuking Mursi.
The result has been a power struggle in a country that is of strategic importance to the United States because of the Suez Canal, a vital conduit for trade and for U.S. military vessels, and because of its peace treaty with Israel.
The United States is in a somewhat delicate position in Egypt, having for three decades strongly supported Mubarak, who worked to repress and to marginalize the Muslim Brotherhood, including at times imprisoning Mursi, now president.
Clinton worked hard not to take sides in the current power struggle, though she made clear she believes the military should ultimately be out of politics.
"The United States supports the full transition to civilian rule with all that entails," she said, commending the Supreme Council of the Armed Forces, the military council that assumed power after Mubarak was ousted on Feb. 11, 2011.
"But there is more work ahead. And I think the issues around the parliament, the constitution have to be resolved between and among Egyptians. I will look forward to discussing these issues tomorrow with Field Marshall Tantawi and in working to support the military's return to a purely national security role."
Although relatively small by recent Egyptian standards, the protest -- which included members of Egypt's Coptic Christian minority as well as secular Muslims -- illustrated deep anger on the part of some of Egypt's population at the Islamists' rise.
"Even Libya did not take the Muslim Brotherhood," said Mony Azba, 47, an engineer carrying an iPhone who wore a medium length skirt and a t-shirt with a Chanel logo.
Accusing Clinton of backing the Muslim Brotherhood, she added: "Why is she pushing (them) here?" (Additional reporting by Yasmine Saleh; Writing by Tom Perry and Arshad Mohammed; Editing by Sophie Hares)