Egyptian jets bombed Islamic State targets in Libya on Monday, a day after the group there released a video showing the beheading of 21 Egyptian Christians, drawing Cairo directly into the conflict across its border.

Egypt said the pre-dawn strike hit militant camps, training sites and weapons storage areas in the neighbouring oil-producing country, where factional fighting has unleashed virtual anarchy and created havens for jihadi Islamists.

While Cairo is believed to have provided clandestine support to a Libyan general fighting a rogue government in Tripoli, the 21 decapitations pushed President Abdel Fattah al-Sisi into open action, expanding his battle against Islamist militancy.

"And let those near and far know that the Egyptians have a shield that protects and preserves the security of the country, and a sword that eradicates terrorism," the Egyptian military said in a statement.

Egyptian state television aired footage of fighter planes leaving a hangar with "Long live Egypt" emblazoned on their tails, followed by night-vision aerial footage showing bomb explosions and the aircraft returning in early daylight.

Libya's air force also participated in Monday's attack, which targeted Derna, an eastern coastal city regarded as a base for fighters of the ultra-radical Islamic State.

"There are losses among individuals, ammunition and the (Islamic State) communication centres," Libyan air force commander Saqer al-Joroushi told Egyptian state television, adding that dozens had been killed.