Security has been stepped up across the country, with officials warning they will deal firmly with protesters.
Discontent has worsened following a recent deal to cede sovereignty over two Red Sea islands to Saudi Arabia.
Mr Sisi has defended his decision, saying the islands of Sanafir and Tiran always belonged to Saudi Arabia.
Secular and leftist activists have called for demonstrations on Monday in defiance of an anti-protest law that bans unauthorised gatherings.
The protests have been scheduled on a holiday that marks the anniversary of Israel`s withdrawal from the Sinai Peninsula in 1982.
"I see there are people calling once again for damage to (Egypt`s) security and stability," Mr Sisi said, repeating that there were "evil" forces conspiring against his country.
"Our responsibility is to protect security and stability, and I promise Egyptians that no one will terrorise them again."
Troops have been deployed to key areas of Egypt`s main cities, and agents have rounded up dozens of activists, journalists and lawyers from their homes and cafes in Cairo.
In a statement, Egypt`s Interior Minister Magdy Abdel Ghaffar said "security forces... will confront with extreme rigour any attempt to disturb public order," the Agence France-Presse news agency reported.
Observers say public dissatisfaction with Mr Sisi has grown recently because of the poor state of the economy and recent alleged cases of abuse by security forces.
As former armed forces chief, Mr Sisi led the army`s overthrow of President Mohammed Morsi, an ex-Muslim Brotherhood official, in 2013 following mass protests.
Since then, more than 1,000 people have been killed and 40,000 are believed to have been jailed in a sweeping crackdown on dissent, most of them from the outlawed Brotherhood.
Local and international human rights activists say the situation in the country has never been worse, with Amnesty International saying Egypt has reverted "back to a police state".