Islamic State calls for attacks to disrupt Egypt elections
The threats were made in a 23-minute video posted late on Sunday on websites known to be sympathetic to the group.
The authenticity of the video could not be verified, but appeared similar to past releases by the group.
It made a brief mention of an ongoing offensive by security forces against IS in the Sinai peninsula, suggesting it was made after the large-scale military campaign began on Friday.
The video also showed what appeared to be footage of past IS attacks in Sinai and the killings of unarmed off-duty soldiers or men suspected of collaborating with security forces.
Egypt's army has pursued Islamic State group militants in the northern Sinai region for years, after numerous bomb and gun attacks on troops in the region.
After a number of military offensives, the group is thought to have been weakened and switched from attacks on the military to softer targets such as mosques and Coptic Christian churches.
Sisi is preparing for March's presidential elections which is widely expected to be a one horse race after the arrests of and pressure on the president's opponents.
But the former general - who vowed to return security to Egypt after a 2013 military coup - will likely be embarrassed by continued attacks.