The Islamist Libyan militia Fajr Libya has called on Egyptian workers to leave the country within 48 hours, reported various media outlets.
Fajr Libya, the post-Ghaddafi armed group that controls the capital Tripoli, said in a statement that their call aims to "protect Egyptian workers from any revenge attacks on them, which will only create a dispute between two brotherly peoples."
The statement comes hours after retaliatory Egyptian airstrikes in eastern Libya against IS group targets left tens of militants dead.
A video released by the Islamic State group on Sunday on YouTube shows the beheading of more than a dozen Egyptian Christians men by the militant group near Tripoli.
Twenty-one Coptic workers, mostly from impoverished villages in Upper Egypt, were kidnapped between late December and early January in the Libyan city of Sirte.
The Libyan armed group also asked Egyptian President Abdel El-Sisi to announce the names of the 21 killed to the world and to allow the press to interview family members of the victims who were beheaded by Islamic State militants.
Since the 2011 toppling of longtime dictator Muammar Gaddafi, Libya has been sinking in chaos as rival militias battle the fight the central government for power.
An internationally-recognised government led by Abduallah El-Thinni resides in the eastern city of Tobruk.
El-Thinni's Cabinet, however, is contested by another Islamist-led government headed by Omar El-Hassi and headquartered in the capital Tripoli.
Fajr Libya, which is a coalition of Islamist-led militias, has controlled Tripoli and a number of western areas since August 2014.
Meanwhile, IS in Libya, which formed in the last two years, maintains control of different patches of the country.
Last year, army forces led by Gaddafi-era Libyan general Khalifa Haftar regained control of the eastern city of Benghazi from Islamist militias.
Haftar's troops were later recognised as the national Libyan army.