CAIRO — The Egyptian military said Monday that it had carried out airstrikes in Libya in retaliation for the beheading of more than a dozen Egyptian Christians by a branch of the Islamic State extremist group there.

In a statement Monday, the Egyptian military said it had conducted airstrikes at dawn against training camps and arms depots of the Islamic State group in Libya, but it did not provide further details.

The foreign ministry said that Egyptian warplanes had struck Derna, a town in eastern Libya that is a hub of Islamist militancy.

It is also close to the Egyptian border, well within the range of the jets.

The airstrikes represent a significant escalation of Egypt’s role in the continuing battle between armed factions in Libya for control of the country.

With the backing of the United Arab Emirates, Egypt has worked covertly to support a Libyan general who is fighting to take back the capital and much of the coast from a rival coalition of militia groups, some of which are made up of Islamist extremists.

In a televised address late Sunday night, President Abdel-Fattah el-Sissi of Egypt vowed that his country would take action to avenge the killings.

“Egypt reserves the right to respond, with the appropriate manner and timing, in order to carry out retribution on those killers and criminals who are stripped of the most basic of human values,” el-Sissi said.

The Egyptian military said in a statement issued around 8:30 a.m. that the dawn strikes were “retribution and response to the criminal acts of terrorist elements and organizations inside and outside the country.”

“We stress that revenge for the blood of Egyptians, and retribution from the killers and criminals, is a right we must dutifully enforce,” the statement said. Egyptian state television showed footage of F-16s taking off in the dark as the statement was read on the air.

The broadcast then showed a video montage of jets, soldiers, tanks and warships, all set against a soaring musical score. It was narrated by a deep male voice, familiar to those who heard military announcements when generals seized power from President Hosni Mubarak four years ago.

“Honor, nation,” the narrator says. “This is the slogan of men who ask for death as a sacrifice for the nation. They are men who do not know the meaning of impossible. They penetrate rocks and mountains, and they challenge difficulties. They race each other for martyrdom, on land, sea and air. Their life is a heroic epic, and their martyrdom a sacrifice for dignity and a pride for Egypt.”

The leader of the Libyan air forces for the anti-Islamist faction, Saqer al-Joroushi, appeared on Egyptian state television and estimated that the strikes had killed “not less than 40 or 50” people.

Egypt’s air assault came less than 12 hours after the main Islamic State group released a video online that appeared to show fighters from the group’s self-proclaimed Tripolitania Province beheading more than a dozen Egyptian Christians.

The Christians were among the thousands of Egyptians who routinely travel across the border to Libya to find work in its oil-rich economy, forging a deep connection between the two neighboring states. About 20 Egyptian Christians disappeared around the coastal city of Surt weeks ago, and last month the Tripolitania Province released a picture showing that it had captured them.

The video of their beheadings Sunday night aroused special horror in Egypt and beyond because it was filmed with the theatrical brutality that has become a trademark of the Islamic State.

Released under the logo of the Islamic State’s media arm and with the title “A Message Signed With Blood to the Nation of the Cross,” the video appeared to show a row of masked fighters dressed in black and with ceremonial knives at their chests parading more than a dozen captives in orange jumpsuits along a Mediterranean beach in western Libya.

Speaking in English, the lead executioner proclaimed in the video that the fighters were part of the larger Islamic State group fighting in Syria, warned that they would allow no safety to “crusaders,” invoked the American military’s burial at sea of Osama bin Laden and alluded to apocalyptic prophecies about a coming battle for Rome. The fighters then forced their captives to the ground, sawed through their necks, and let the blood darken the waves.

The video appeared to show a greater degree of communication and collaboration between the Islamic State and its Libyan satellite group than Western officials previously had known.