The Israeli army's coordinator went on to say in his video: "Just to be clear, Israel will respond forcefully and resolutely to any Islamic Jihad reaction whatsoever - not just against Jihad, but also against Hamas".
Israel said that the tunnel, which ran from the besieged Palestinian enclave into Israeli territory, was a "terror tunnel" aimed to attack Israelis.
Hamas is allied with Islamic Jihad, which maintains a strong presence in the Gaza Strip.
In the video, Mordechai said Israel is aware of Islamic Jihad attack plans, warning the group of a "harsh and determined Israeli response".
The United States considers Islamic Jihad to be a terrorist organization as well.
"We will take a very firm stance against anyone who tries to attack us or attacks us from any area".
A member of Palestinian security forces loyal to Hamas gestures while searching for missing or dead militants after Israel blew up a cross-border tunnel, in Khan Younis in the southern Gaza Strip November 3, 2017.
Israeli Prime Minister Benjamin Netanyahu on Sunday threatened to respond harshly if Gaza militants will revenge Israel's deadly bombing of a tunnel that crossed into Israel last month.
Israel's army has deployed anti-rocket Iron Dome batteries in central Israel, a military spokesperson said in a statement on Monday.
The Gaza front has been relatively peaceful for Israel since 2014 when more than 2100 Palestinians and 70 Israelis were killed in a 50-day war.