A video emerged on Sunday showing what appeared to be the beheading of 21 Egyptian Christians who had been kidnapped by Islamic State (IS) militants in Libya.
The footage shows a group wearing orange overalls, being forced to the ground and then decapitated.
IS militants claim to have carried out several attacks in Libya, which is in effect without a government since the overthrow of Muammar Gaddafi in the 2011 uprising.
Egyptian President Abdel Fattah al-Sisi warned that his country would respond to the deaths as it saw fit.
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".
Egypt's state news agency MENA quoted the spokesman for the Coptic Church as confirming that 21 Egyptian Christians believed to be held by Islamic State 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 U.S.-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.
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 Coptic Church said it was confident the government would seek justice. Al Azhar, the centre of Islamic learning in Egypt, said no religion would accept such "barbaric" acts.
UK Foreign Secretary Philip Hammond condemning the beheadings said "Such barbaric acts strengthen our determination to work with our partners to counter the expanding terrorist threat to Libya and the region.”
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