Adel Emara, a member of the SCAF, said the military was investigating the incident.
The Scaf said it was confident "all state institutions" would respect the law and constitution.
But the SCAF now seems to have gone back on its earlier promise to withdraw to its barracks.
The new defence minister, Abdel Fattah al-Sisi, is a young member of the SCAF who ran its intelligence department.
Not surprisingly, many Egyptians are crying foul, describing the SCAF's dodgy refereeing as a power grab or soft coup.
Since then, however, the generals' Supreme Council of the Armed Forces (SCAF) has made a hash of just about everything.
Thus, the real political equation in Egypt is not now nor never has been the MB versus Mubarak's regime or SCAF.
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Some Egyptians suspect that, in order to avoid confrontation, the Muslim Brothers and SCAF could join forces to back a consensus candidate.
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"(Morsi) doesn't have the power -- SCAF has the power, " he said.
But Pentagon Press Secretary George Little said U.S. officials expect that SCAF "will transfer full power to a democratically elected civilian government, " as it had promised.
We had spoken to many Egyptians who resented the re-occupation of the square and the march on SCAF headquarters that produced street clashes 10 days ago.
The parliament, mired in bickering and thwarted by the SCAF from doing much, was summarily dissolved on the eve of the presidential election by a court order.
Salma Othman, who was protesting Tuesday in Tahrir Square, told CNN she found it "extremely provocative" for the SCAF to suggest it was considering granting a military funeral.
However, unlike Mubarak, SCAF is only in power because the mobs of protesters in Tahrir Square demanded that Mubarak stand down to enable civilian, majority rule in Egypt.
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As things stand, the SCAF will press on with planned elections - whether or not the new parties are ready - and the Brotherhood will carry on consolidating its organisation.
The ruling military - the Supreme Council of the Armed Forces (Scaf) - headed by Field Marshal Tantawi, has been under pressure to bring forward the election date to May.
While SCAF has tried to talk the talk of the new era, all of its members rose through the ranks of the Egyptian military with the blessings of Hosni Mubarak.
The re-appointment of Field Marshal Tantawi, head of the Supreme Council of the Armed Forces (Scaf), is in line with an interim constitutional declaration issued after June's presidential election run-off.
He fears the situation is sidelining weaker factions who don't have the resources to challenge the decisions and allows the SCAF to play one side against the other to its own benefit.
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The Supreme Council of the Armed Forces, or SCAF, is still a little hazy about the dates of elections but it seems that those or the country's parliament will happen in late November.
Many Egyptian politicians and analysts, accustomed to attributing moves by the SCAF to efforts to extend its own political power or block Islamists, struggled to divine a clear political motive for the disqualifications.
Because SCAF is comprised of the men who served as Mubarak's underlings throughout his 30-year rule, it shares many of the institutional interests that guided Mubarak and rendered him a dependable US ally.
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"We have and will continue to urge the SCAF to relinquish power to civilian elected authorities and to respect the universal rights of the Egyptian people and the rule of law, " he told reporters.
"It is not a political move or a decision by the SCAF, it is a legal matter that has been referred to the tribunal, by individuals, by other parties, " he told CNN's Christiane Amanpour.
Since Mubarak stepped down on February 11, 2011, SCAF has stumbled from one crisis to another, reacting with violence and brutality against protesters, but often ceding ground when Tahrir Square filled and passions boiled.
Although he played a prominent role in the Egyptian uprising that toppled Hosni Mubarak's regime and is a vocal critic of the Scaf's policies, his left-leaning politics have been eclipsed by the leading Islamist parties.
The army said it has handed most of its executive powers to Mr. Ganzouri and his newly appointed cabinet, but demonstrators have demanded that SCAF yield all of its power to a civilian president or council.
But it was not clear how far the generals, members of the Scaf, actually consented to a move that re-orders the country's political forces and gives Mr Mursi more powers while a new constitution is mooted, correspondents say.
However, Gen Mohammed al-Assar, a member of the Supreme Council of the Armed Forces (Scaf), told the Reuters news agency the decision had been "based on consultation with the field marshal, and the rest of the military council".
The Supreme Council of the Armed Forces (SCAF), a cabal of a score or so of generals who became the caretaker rulers after Mr Mubarak's fall, has never been keen to let Egypt become a fully fledged democracy.
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