Egypt's military said in a statement on state television it had carried out an air strike against Islamic State targets in Libya at dawn on Monday, a day after the group released a video appearing to show the beheading of 21 Egyptians there.

The attack focussed on Islamic State camps, training sites and weapons storage areas in Libya, where Islamist militants have thrived amid chaos.

President Abdel Fattah al-Sisi has repeatedly said militants based in Libya pose a serious security threat to Egypt, a strategic US ally that is fighting insurgents in the Sinai who have pledged allegiance to Islamic State.

The 21 Egyptian Christians, who had gone to Libya in search of jobs, were marched to a beach, forced to kneel and then beheaded, the video showed.

Fench President Francois Hollande condemned the "savage" killings and said France and its allies were determined to fight the militants.

"He expresses his concern about the extension of Daesh [ISIS] operations in Libya and reminds of the determination of France and its allies to fight against this group," Hollande's office said.

The White House also condemned the "despicable and cowardly murder" and urged a political solution to the conflict in the country.

"This wanton killing of innocents is just the most recent of the many vicious acts perpetrated by ISIL-affiliated terrorists against the people of the region, including the murders of dozens of Egyptian soldiers in the Sinai, which only further galvanizes the international community to unite against ISIL," said White House spokesman Josh Earnest.

"This heinous act once again underscores the urgent need for a political resolution to the conflict in Libya, the continuation of which only benefits terrorist groups, including ISIL."

Egyptian President Abdel Fattah al-Sisi warned on Sunday that his country would respond to the "criminal killings" as it saw fit.