El-Sissi told the audience, which included families of troops killed during the 1973 war and in recent violence, that the armed forces will not support any candidate for the presidency.
"The armed forces will not support any single" candidate, el-Sissi said in comments aired on state TV and carried by other private stations. "Everyone has to face the people who will decide ... not the army."
"You people will choose your rulers, and true, you are the ones who get rid of them too," said el-Sissi, a reference to the huge demonstrations that helped push Morsi, as well as his predecessor Hosni Mubarak, from office.
El-Sissi called for "a quick conclusion to the transitional period according to the measures agreed upon in the road-map," according to the official Middle East News Agency. "There must be an accord to quickly return to work, stability and confronting the challenges to Egypt's national security."
An appointed committee is nearly finished with the task of amending the constitution, the first step in the post-July 3 road map. Officials in the committee say a first draft of the charter is expected by mid-October. Parliamentary and presidential elections are to follow the adoption of the amended charter in a referendum, expected by late February or early March, capping the road map announced by el-Sissi.
Pro-Morsi protests have weakened, but continued on a near-daily basis, since his fall. Meanwhile, authorities have battled with a surge in militant activities in northern Sinai and in other parts of Egypt. They accuse Morsi supporters of fueling the violence to unsettle the interim authorities. The pro-Morsi camp has denied the charges.
In his speech, el-Sissi saluted troops and the police force for their role in fighting the violence.
In a rare gesture, el-Sissi also apologized to the residents of Sinai, whom he said may have suffered some losses or damage during the ongoing military operation against militants in the area bordering the Gaza Strip and Israel. El-Sissi vowed to compensate the residents for the losses they incurred.
Some residents of Sinai have complained of what they said were arbitrary raids that impacted civilians.