Mursi says the constitution and an upcoming vote to re-elect the lower house of parliament will help end squabbling among feuding politicians.
Cabinet resignations deal setback for Egypt's MursiHenry represents Anglican Christians in Egypt. In a letter published by state media, she said minority groups were not represented properly in the chamber.
Mubarak, who was sentenced to life in prison in June, was moved to an army hospital on Thursday following a fall that raised concerns about his fragile health.
The strife has cast doubt on the government's ability to push through the spending cuts and tax hikes needed to secure a vital $4.8 billion International Monetary Fund loan.
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"I have reached a clear conclusion that a lot of the policies and efforts contradict my personal beliefs and I don't see them as representative of our people's aspirations," he said in his resignation letter, which has yet to be accepted by the prime minister.
Egypt's defense chief said the army - which dominated Egypt for decades and has wide ranging business interests - was ready to step in to help the economy.
The 270-seat upper house, or Shura Council, holds legislative authority until a new parliament is elected in early 2013. Opposition figures say they fear the Council could issue laws curbing freedoms.
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CAIRO (Reuters) - An Islamist minister quit Egypt's government on Thursday, the second cabinet resignation this week, as President Mohamed Mursi tries to shore up his authority and gather support for unpopular austerity measures.
Under pressure to acknowledge Egypt's diversity, Mursi appointed 90 members including Christians, liberals and women to the Council - alongside figures from the Muslim Brotherhood and ultra-conservative Salafis - last week. Two-thirds of the upper house were already elected in a vote this year.
Neither were major figures in the cabinet but their decision to criticize the substance and style of Mursi's administration suggests his decisions are unnerving not just opponents but also some allies.
Rivals accuse Mursi, who won Egypt's first freely contested leadership election in June, of polarizing society by foisting a divisive, Islamist-leaning constitution on the country and using the autocratic ways of his deposed predecessor Hosni Mubarak.
"The Egyptian economy is going through a very difficult stage," Abdel Fattah al-Sisi was quoted as saying by state news agency MENA. "The armed forces are keen to participate in development and service projects in all parts of Egypt as part of its promise to serve the great people."
The charter crafted by an Islamist-dominated assembly is meant to be the cornerstone of a democratic and economically stable Egypt after decades of authoritarian rule. The opposition says it does nothing to protect minorities.
Deadly violence preceded a referendum on the basic law, dealing a blow to a struggling economy. Mursi's political rivals refused to accept the result - the text won about 64 percent in the vote - and they reject his call for national unity talks.
"We stress again that the nation should achieve internal reconciliation and forget its differences," the Muslim Brotherhood's supreme guide, Mohamed Badei, told Egyptians in his weekly message.
Mursi is also promising incentives aimed at making Egypt - once a darling of emerging market investors - an attractive place to do business again.
In a move that may pre-empt a planned reshuffle, parliamentary affairs minister Mohamed Mahsoub announced he was quitting because he disagreed with the slow pace of reform.
Communications Minister Hany Mahmoud quit earlier this week, citing his inability to adapt to the government's "working culture".
Her resignation underscores fears by Egypt's Christians, who make up about a tenth of its 83 million population, about the gains by Islamists since Mubarak was ousted in 2011.
The Egyptian pound tumbled to its weakest in almost eight years against the dollar this week as people rushed to withdraw savings from banks.
(Writing by Maria Golovnina; Editing by Tom Pfeiffer)
"Let's work seriously to end the reciprocal wars of attrition. We urgently need to unify ranks and group together and focus our capabilities and assets for the general benefit."
Earlier on Thursday, a Christian member of Egypt's upper house of parliament, Nadia Henry, quit a day after the Islamist-dominated chamber took over legislative authority under the new constitution.
He and his Muslim Brotherhood allies say ordinary people are fed up with street protests that often turn violent and want the government to focus on urgent bread-and-butter issues.
An economic crisis and a battle over a new constitution have underlined bitter divisions between Islamist-backed Mursi and his liberal opponents and delayed a return to stability almost two years since a popular uprising.
The resignations come ahead of a promised cabinet reshuffle. Cabinet sources told Reuters as many as eight cabinet members from second-tier ministries might go next week.
