"Within the next few hours, the Egyptian and Libyan air forces will carry out new airstrikes on Islamic State positions near the town of Sirte," Libyan military spokesman Ahmed Al-Mismari was quoted as saying by Egypt's Al-Masry Al-Youm newspaper.
On Sunday evening, the IS published a video showing the beheading of 21 Egyptian Coptic Christians who were kidnapped in Libya.
Egyptian President Abdel Fattah Sisi said Cairo "reserves the right to respond in any way" after the brutal killings.
Earlier on Monday the air forces of the two countries conducted coordinated airstrikes against the insurgents near the city of Derma, Libya, reportedly destroying five buildings.
Following the publication of the execution video, Egypt urged the members of the US-led anti-IS coalition to help the country combat the militant group in Libya.
The Islamic State is a militant group in control of large areas of Syria and Iraq. The group has published numerous videos of executions of captive foreigners.
A coalition led by Washington is currently conducting airstrikes against the extremists in Iraq and Syria.