Earlier this week, the area around the palace was the scene of the worst civilian clashes since Morsi came to power.
In an attempt to calm the situation, Morsi called for Saturday's dialogue. But the main opposition leaders refused to attend, saying it didn't address their main demands and was being held under the threat of violence against protesters.
"No reasonable person would agree to be part of a dialogue held at the point of a sword," the National Salvation Front said in a statement.
The crisis began Nov. 22 when Morsi granted himself authority free of judicial oversight, mainly because he feared a looming court decision that was expected to declare the Islamist-led constitutional drafting assembly illegal and order it disbanded. The assembly then quickly adopted a draft constitution despite a walkout by Christian and secular members.
The moves touched off a new wave of opposition and unprecedented clashes between the president's Islamist supporters, led by the Muslim Brotherhood, and protesters accusing him of becoming a new strongman.
With the specter of more fighting among Egyptians looming, the military sealed off the presidential palace plaza with tanks and barbed wire.
State media also reported that the government was working on a new law to allow the military to arrest civilians, but there was no official word on that either.
The state-owned Al-Ahram newspaper quoted an unnamed military official as saying the move would be "preventive" if the situation worsened.
The report could not be independently confirmed and the law would have to be signed by Morsi before it takes effect.
At the presidential palace sit-in on Saturday, TV footage showed the military setting up a new wall of cement blocks around the palace.
Muslim Brotherhood spokesman Mahmoud Ghozlan accused the opposition of seeking the military's return to politics by "pushing matters to the brink."
He said the military statement showed it agrees on the legitimacy of the elected president, the referendum plans and state institutions, and will protect them from any "attack."
The group's top leader Mohammed Badie and his powerful deputy Khairat el-Shater, meanwhile, held news conferences alleging a conspiracy to topple Morsi, although they presented little proof.
Badie said the opposition, which has accused his group of violence, is responsible for attacks on Muslim Brotherhood offices. He also claimed that most of those killed in last week's violence at the palace and other governorates were Brotherhood members.
"These are crimes, not opposition or disagreement in opinion," he said.
Meanwhile, the opposition accused gangs organized by the Brotherhood and other Islamists of attacking its protesters, calling on Morsi to disband them and open an investigation into the bloodshed.
Meanwhile, with dialogue boycotted by the main opposition players, members of a so-called Alliance of Islamists forces warned it will take all measures to protect "legitimacy" and the president — comments that signal further violence may lie ahead.
Mostafa el-Naggar, a former lawmaker and protest leader during the uprising that led to Mubarak's ouster in February 2011, said the Brotherhood and military statements suggested the crisis was far from over.
"As it stands, Egypt is captive to internal decisions of the Brotherhood," he said.