Cairo has carried out air strikes against Islamic State group targets in Libya after the jihadists posted a video showing the beheadings of 21 Egyptian Christians.

Egypt said a "tough intervention" was needed and with France called on the UN Security Council on Monday to "take new measures" against the jihadists in neighbouring Libya.

With the air strikes, Egypt opened a new front against the jihadists. Cairo is already battling militants in the Sinai Peninsula where scores of troops have been killed since the army toppled Islamist president Mohamed Morsi in July 2013.

President Abdel Fattah al-Sisi, the former army chief who overthrew Morsi and has been criticised for a deadly crackdown on dissent, has presented Egypt as a crucial partner in international efforts against the jihadists.

The air strikes hit IS camps and weapons depots, the military said, hours after jihadists released gruesome footage of the beheadings that provoked outrage in Egypt.

Witnesses told AFP there were at least seven strikes in Derna in the east, a hotbed of militancy since Libyan dictator Moamer Kadhafi was overthrown in 2011.

"Your armed forces on Monday carried out focused air strikes in Libya against Daesh camps, places of gathering and training, and weapons depots," the military said, using the pejorative Arabic acronym for IS.

Libyan air force chief Saqr al-Jaroushi told an Egyptian broadcaster at least 50 people were killed, a toll which could not be confirmed, and that Libyan warplanes also targeted the jihadists.

It was the first time Egypt announced military action against Islamist targets in Libya. Last year Cairo reportedly allowed the United Arab Emirates to use its bases to bomb militants there.

Experts say that by targeting IS with air strikes in Libya, Sisi has become a key ally of the West against Islamist extremists, despite international condemnation of his crackdown against the Muslim Brotherhood of president Mohamed Morsi, who was ousted by Sisi in 2013.

IS militants have been hammered by US-led air strikes in Iraq and Syria after taking over swathes of the two countries, and the group has active affiliates in Egypt and Libya.

Bombing IS targets in Libya will now show Sisi's resolve to counter a wider Islamist threat in the region, said H.A. Hellyer, Arab affairs expert at Washington-based Brookings Institute.

- Mourning families -

"Avenging Egyptian blood and retaliating against criminals and killers is a duty we must carry out," the military said.

The raids came after Sisi threatened a "suitable response" to the killing of the Christians.

Foreign Minister Sameh Shoukry was headed to Washington to take part in an anti-terrorism summit, his ministry said, urging strong international action.

"Leaving matters as they are in Libya without tough intervention to curb these terrorist organisations represents a clear threat to international security and peace," the ministry said.

The killing of the Christians, who like thousands of Egyptians had travelled abroad to seek work, shocked their compatriots.

"Revenge is on the way," read the front-page banner of the official Al-Akhbar newspaper. Both the Coptic Church and the prestigious Islamic Al-Azhar institution condemned the attack.

In the village of Al-Our in Upper Egypt, where 14 of the victims were from, devastated family members gathered in church.

"My son travelled to Libya 40 days ago, he wanted to make money for his marriage," said Boshra, whose 22-year-old son Kirollos was among the dead.

Expressing his "profound sadness," Pope Francis said the Copts "were executed for nothing more than the fact that they were Christians".

Egyptian television repeatedly played the video without the beheadings, showing black-clad militants leading their captives in orange jumpsuits along a beach before forcing them to kneel.

The White House led condemnation of the beheadings, saying the killers were "despicable".

President Francois Hollande of France agreed with Sisi that "the Security Council meet and that the international community take new measures to face up to this danger".

France on Monday signed its first export contract for Rafale fighter jets with Egypt.

The European Union said it will meet with the Egyptian and US governments this week to discuss joint action on Libya, but that it saw no role in any military intervention for now.