"If the Sinai Province tried to target our citizens and soldiers, we will make sure we hit them forcefully and decisively," said Brigadier General Royi Elcabets.
The commander was quoted on Wednesday by Israeli army spokesman Avichay Adraee, who posted the remarks on his Facebook page. The statement was made during a military ceremony marking the transfer of command from Elcabets to Rafi Miloa, the new head of the southern Adom formation.
"There have been significant changes on the other side of the border that require us to be ready for any scenario or downslide, and to continue securing our southern area," the new commander added.
Based in the Sinai Peninsula, the Sinai Province (Waliyat Sinai) pledged allegiance to the Islamist State group in November 2014.
The group is known for claiming responsibility for Egypt's deadliest and bloodiest attacks in Sinai last July.
Earlier this month, 21 soldiers were killed during simultaneous militant assaults on army checkpoints in the North Sinai towns of Sheikh Zuweid and Rafah, an attack that prompted days-long fighting between troops and insurgents and left over 200 militants dead.
The group also claimed responsibility in July for a rocket attack launched from the Sinai Peninsula into southern Israel.