The decision to retire the top generals was taken in coordination and consultation with the army, a military source said, adding the armed forces are a professional and deeply- rooted institution that will always belong to the people.
He expressed appreciation for the role played by defence minister Tantawi and Lt Gen Sami Anan following the January 25 revolution that ousted longtime president Hosni Mubarak.
Commenting on decisions to change armed forces top commanders, Morsi asserted that his step was aimed to serve Egypt's interests.
"I wish luck for the Armed Forces and to be free for their sacred mission in protecting the nation," Morsi added.
The presidency denied Tantawi and Anan are under house arrest as claimed by some media. The presidency also stressed they remain to be part of the presidential team as advisors.
Meanwhile, the Salafist Front expressed support for Morsi's steps, calling on its loyalists to take to streets to show their backing.
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The group recalled in a statement that "it was the first to call for taking this step particularly after the regrettable incidents of Rafah" where 23 soldiers were killed and wounded when terrorists attacked them.
The Revolution's Board of Trustees also backed the president's decision, terming it as historic. "Morsi is Egypt's first president to return the civil face to the country after a six-decade absence," it said in a statement.
It called on the president to accomplish the other goals of the revolution by taking such brave decisions to purge the judiciary and the media.
Al-Wasat party leader Abu-al-Illa Madi today said Morsi's decision was a real prelude to rebuild Egypt on civil and democratic bases. In Qalyubia, political powers and Islamist trends welcomed the president's decisions.
Scores of Freedom and Justice Party's members organized rallies in separate places in the governorate to show support for Morsi's unexpected step.
The Egyptian Revolutionaries Coalition also announced support for the president's decisions particularly to annul the complementary constitutional declaration.
Right after the surprise reshuffle, state-run news agency MENA quoted an unnamed military official as saying that there has been no "negative reaction" from within the military.
And a day after the orders, no unusual military movements were detected anywhere across the nation. If Morsi's decisions go unchallenged, it should end the power struggle that pitted him against the powerful military. That could mean the ushering out of six decades of de facto military rule since army officers seized power in a coup in 1952.