The military said serious dialogue is the only way to overcome the nation's deepening conflict over a disputed draft constitution adopted by Islamist allies of President Mohammed Morsi, and recent decrees granting himself near-absolute powers.
"Anything other than that (dialogue) will force us into a dark tunnel with disastrous consequences; something which we won't allow," the statement said. It was read by an unnamed military official on state television.
Morsi had called for a dialogue on Saturday to discuss ways to resolve the disagreement. His vice president suggested that a Dec. 15 constitutional referendum could be delayed.
However, opposition leaders declined to attend, saying that talks can only take place if Morsi rescinds his decrees and cancels the referendum.
Most of the public figures at the meeting were Islamists, and at least three members left the talks soon after they started. A lawyer among them said it was a one-way conversation, accusing the presidential advisers of refusing to listen.
Egypt's military, which temporarily took over governing the country after the revolution that ousted autocratic leader Hosni Mubarak, was largely sidelined weeks after Morsi was elected.
After he was sworn in, Morsi ordered the two top generals to retire and gave himself legislative powers that the military had assumed in the absence of a parliament, which had been dissolved by the courts.
The current crisis started Nov. 22 when Morsi granted himself authority free of judicial oversight, saying judges loyal to the former regime were threatening the constitutional drafting process and the transition to democracy.
However, the move sparked opposition and clashes between the president's Islamist supporters led by the Muslim Brotherhood and protesters accusing him of becoming a new strongman.
At least six civilians have been killed and several offices of the president's Muslim Brotherhood torched in the unrest. The two sides also have staged a number of sit-ins around state institutions, including the presidential palace where some of the most violent clashes occurred.
Saturday, protesters once again gathered outside the palace. They won something of a victory on Friday, when Morsi agreed to delay voting on the controversial draft constitution.
The draft was produced by pro-Morsi Islamists with no input from other groups. It could be re-negotiated, now that the referendum has been delayed.
The Associated Press contributed to this report.