(CNN) -- Egyptian President Mohamed Morsy has won praise for his government's effort to bring about a cease-fire between Israel and Hamas, a delicate balancing act for the country's nation's first freely elected leader. Egypt has been the go-between in many previous Israeli-Palestinian disputes. But while longtime Egyptian strongman Hosni Mubarak was hostile to Hamas, the Palestinian Islamist movement that rules Gaza, Morsy's Muslim Brotherhood is the group's political cousin. And although Morsy leads a population with deep historical sympathy for the Palestinians, he has pledged to maintain Egypt's peace treaty with Israel. "He has clearly recognized Egypt's national interest here, and hopefully this can succeed and take hold," said George Mitchell, the former U.S. Senate majority leader and Obama administration Middle East envoy.
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NEW: Mohamed Morsy "clearly recognized Egypt's national interest," George Mitchell says
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NEW: Egypt "behaved responsibly" in talks, Hamas leader says
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Brokering the cease-fire was a delicate balancing act for Egypt's recently elected leader
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"Hamas listens to Mohamed Morsy," one analyst says
Under Mubarak, the country's security forces had suppressed its own Islamists in the @placeholder, even jailing Morsy at one point.