The army chief's comments suggested the military's impatience with politicians' power struggles.
"The continuation of the conflict between the different political forces and their differences over how the country should be run could lead to the collapse of the state and threaten future generations," el-Sissi said, speaking to military cadets in comments posted on the armed forces' Facebook page.
He also spoke of a "realistic threat" facing the nation from its mounting political, economic and social problems.
El-Sissi was appointed by Morsi as military chief and defense minister last autumn when the president sidelined the armed forces' top brass, who had ruled the country for nearly 17 months following Mubarak's fall.
El-Sissi is widely believed to be against direct rule by the generals, seeing it as damaging to the armed forces' reputation. Throughout Morsi's 7-month-old administration, he and the Islamist leadership appear to have reached an understanding on working together.
There was an earlier instance when el-Sissi appeared to feel compelled to intervene in politics, when he invited politicians to an informal gathering to ease tensions amid protests and clashes in November and December. The gathering was called off and some Brotherhood officials later suggested they felt el-Sissi had overstepped his bounds.
His comments Tuesday raise the question of how strongly the armed forces will support Morsi if no resolution is found.
In Port Said, many residents said Morsi and the Brotherhood had shown they were not qualified to govern.
"Port Said has fallen from Morsi's grip," Ibrahim Nasr, an activist, said. "The calls for independence are a message to Morsi to forget about the Canal cities."