Egypt's President Abdel Fattah al-Sisi has called for a United Nations resolution allowing international forces to intervene in Libya.
There was no other choice, he told French radio. "We will not allow them to cut off the heads of our children."
Egyptian jets bombed IS targets on Monday in response to a militant video of the apparent beheadings of 21 Egyptian Christians.
Rival militias have been battling for control in Libya since 2011.
Numerous militia groups have battled for control and two rival governments are operating, in Tripoli and Tobruk.
Mr Sisi called for weapons to be made available to Libya's internationally recognised government, which fled to Tobruk after rival militias seized power in the capital.
"We abandoned the Libyan people as prisoners to extremist militias," Mr Sisi told Europe 1 radio. He was referring to the aftermath of the 2011 war in which Libyan leader Muammar Gaddafi was toppled with the help of an international coalition.
That intervention was "an unfinished mission", he said.
Asked if he would order Egypt's air force to strike again, he said: "We need to do it again, all of us together."
Egypt signed a €5.2bn (£3.8bn) defence deal with France on Monday which includes the purchase of 24 advanced fighter jets.
Egyptian state TV said Monday's air strikes had targeted Islamic State camps, training sites and weapons storage areas near the city of Derna.
Military sources said the strikes would continue but there was no need for ground troops at present.
The attacks came hours after a video emerged on Sunday showing militants forcing a group of men to the ground and decapitating them.
The kidnapped Egyptian workers, all Coptic Christians, were seized in separate incidents in December and January from the coastal town of Sirte in eastern Libya, which is under the control of Islamist groups.
The BBC's Jim Muir says anger has been felt throughout Egypt by Muslims and Christians alike, and the killings are being seen as an attack on national dignity.
Egypt is already fighting Islamist insurgents based in the Sinai peninsula who have declared their allegiance to ISIS.
Libya is home to a large community of both Muslim and Coptic Egyptians, with most working in the construction sector.
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