Speaking on national television hours after the release of the video, Sisi said Cairo would choose the “necessary means and timing to avenge the criminal killings”, Reuters reports.
Egypt's state news agency MENA quoted the spokesman for the Coptic Church as confirming that 21 Egyptian Christians believed to be held by ISIS were dead.
The beheadings could stiffen Sisi's resolve in dealing with security threats from militants thriving in neighbouring Libya's chaos who want to topple his US-backed government.
Egypt has denied reports in the past that it had taken part, along with its close ally the United Arab Emirates, in air strikes against militants based in Libya.
The footage showing the deaths of the Egyptians appeared on the Twitter feed of a website that supports ISIS, which has seized parts of Iraq and Syria and has also beheaded Western hostages.
In the video, militants in black marched the captives, dressed in orange jump suits, to a beach the group said was near Tripoli. They were forced down onto their knees, then beheaded.
A caption on the five-minute video read: “The people of the cross, followers of the hostile Egyptian church.” Before the killings, one of the militants stood with a knife in his hand and said: “Safety for you crusaders is something you can only wish for.”
Thousands of Egyptians desperate for work have travelled to Libya since an uprising at home in 2011, despite advice from their government not to go to a country sliding into lawlessness.
Sisi, who met with the country's top military commanders to discuss the killings, called for a seven-day mourning period, state television reported.
The United States on Sunday condemned the “despicable and cowardly murder” of the 21 Egyptians.
“This wanton killing of innocents is just the most recent of the many vicious acts perpetrated by ISIL-affiliated terrorists against the people of the region, including the murders of dozens of Egyptian soldiers in the Sinai, which only further galvanises the international community to unite against ISIL,” White House spokesman Josh Earnest said, using an acronym for ISIS.
The Coptic Church said it was confident the Egyptian government would seek justice. Al Azhar, the centre of Islamic learning in Egypt, said no religion would accept such “barbaric” acts.
The families of the kidnapped workers had urged Cairo to help secure their release. In the mostly impoverished southerly Minya Governorate, relatives screamed and fainted upon hearing news of the deaths.
Egypt, the most populous Arab state, has not taken part directly in the US-led air strikes against ISIS targets in Iraq and Syria, focusing instead on the increasingly complex insurgency within its own borders.
Militants based in Libya changed its name from Ansar Beyt al-Maqdis and pledged allegiance to ISIS.
Militants based in Libya have made contact with Sinai Province, a group operating from Egypt's Sinai Peninsula that has changed its name from Ansar Beyt al-Maqdis and pledged allegiance to ISIS.
The group has killed hundreds of Egyptian soldiers and police since the army toppled Islamist president Mohamed Morsi in 2013 after mass protests against his rule.
With Libya caught in a chaotic power struggle between two rival factions operating their own governments, Western officials worry that extremist militants are taking advantage of the turmoil to strengthen their presence.
A number of Islamist militant groups have been active since the fall of Muammar Gaddafi in 2011 left Libya without a strong central government. A few have declared ties to the radical ISIS and claimed high-profile attacks over recent weeks in what appears to be an intensifying campaign.