A spokesman for the Armed Forces General Command announced the strikes on state radio Monday, marking the first time Cairo has publicly acknowledged taking military action in neighboring Libya, which has been beset by militia violence for months.
The statement said the warplanes targeted weapons caches and training camps before returning safely. It said the strikes were "to avenge the bloodshed and to seek retribution from the killers."
"Let those far and near know that Egyptians have a shield that protects them," it said.
Egypt called for a seven day period of mourning over the death of 21 Egyptian Christians, beheaded by Isis militants, and warned it would "avenge the criminal killings."
A still from the video, which appears to show Isis militants beheading 21 hostages. Photo / Screengrab
Sisi said Cairo would choose the "necessary means and timing to avenge the criminal killings".
Thousands of Egyptians desperate for work have traveled 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.
Last week, Cairo began to evacuate all Egyptian citizens wishing to return from Libya, and has renewed a travel alert to the neighbouring country.
Militants in Libya had been holding the 21 Egyptian Coptic Christians hostage for weeks, all laborers rounded up from the city of Sirte in December and January.
The makers of the video identify themselves as the Tripoli Province of the Islamic State group.
Libya has seen a rise of powerful armed militias in the wake of the downfall and death of dictator Muammar Gaddafi in the 2011 NATO-backed uprising.
The video, released late Sunday night (local time), depicted several men in orange jumpsuits being led along a beach, each accompanied by a masked militant. The men are made to kneel and one militant, dressed differently from the others, addresses the camera in North American-accented English.
"All crusaders: safety for you will be only wishes, especially if you are fighting us all together. Therefore we will fight you all together," he said. "The sea you have hidden Sheikh Osama Bin Laden's body in, we swear to Allah we will mix it with your blood."
The men are then laid face-down and simultaneously beheaded.
Read more: The anatomy of a failed hostage rescue deep into Islamic State territory
The militant speaker then pointed northward and said, "We will conquer Rome, by Allah's permission."
Militants in Libya had been holding 21 Egyptian Coptic Christians hostage for weeks, threatening them with death. The makers of the video identify themselves as the Tripoli Province of the Islamic State group - the Islamic militant group that controls about a third of Syria and Iraq.
The Associated Press could not immediately independently verify the video.
The Egyptian government declared a seven-day mourning period and President Abdel Fattah el-Sissi convened an emergency national security meeting to discuss a response.
El-Sissi sent condolences to "the victims of terrorism," according to a statement released by the presidency.
Qalini Sanyout, whose two nephews were among the hostages, answered the phone Sunday night amid the sound of wailing in the background.
"What can we say? Can someone tell us if this is true." he said repeatedly. "The whole village is in mourning. Men are covering their heads with dust and mud."
- Great sorrow -
In a statement, Al-Azhar - the prestigious Cairo-based seat of Islamic learning - said it had heard the news of the beheadings "of a group of innocent Egyptians with great sorrow and grief".
"Al-Azhar stresses that such barbaric action has nothing to do with any religion or human values."
The latest Isis video comes just days after the jihadists released footage showing the gruesome burning alive of a Jordanian pilot the group captured after his F-16 came down in Syria in December.
The highly choreographed video showing the killing of Maaz al-Kassasbeh triggered global outrage.
The video, entitled "A message signed with blood to the nation of the cross", has a scrolling caption in the first few seconds referring to the hostages as "People of the cross, followers of the hostile Egyptian Church".
One of the masked captors, wearing a military uniform and pointing a knife to the camera said in English: "Today we are in the south of Rome, in the land of Islam Libya... the sea you have hidden Sheikh Osama bin Laden's body in, we swear to Allah we will mix it with your blood."
Al-Qaeda founder Bin Laden was shot and killed in a dramatic helicopter raid by US special forces in Pakistan in the early hours of May 2, 2011 and later buried at sea in an unidentified location.
After the beheadings shown today, a scrolling caption on the footage said: "The filthy blood is just some of what awaits you, in revenge for Camilia and her sisters."
- 'We will take revenge' -
A background voice believed to be IS spokesman Abu Mohamed al-Adnani says: "We swear to Allah we will take revenge, even if it takes a while."
Egyptian women Camilia Shehata and Wafa Constantine were the wives of Coptic priests whose alleged conversion sparked a sectarian dispute in Egypt in 2010.
Shehata went missing for five days in July that year after a domestic argument before police found her and escorted her back home.
When she went missing, Coptic Christians staged protests, but when she was returned, Islamists took to the streets alleging she had willingly converted to Islam and was being held by the church against her will.
Wafa Constantine also went missing, in 2004, reportedly after her husband refused to give her a divorce. She was temporarily sequestered at a convent as reports of her conversion were circulated.
In January, the Isis branch in Libya claimed it had abducted 21 Christians.
A spokesman for the Egyptian foreign ministry confirmed to AFP in Cairo at the time that 20 Egyptians had been kidnapped in two separate incidents.
Badr Abdelatty did not say when they were seized or specify their religious affiliation, but said seven Egyptians and 13 others abducted separately in Libya "are still being detained" by their captors.
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