"Prime Minister Benjamin Netanyahu and I have instructed the IDF to act with full force, both on the ground and from the air, including during the ceasefire, in order to protect our soldiers in Lebanon from any threat," Katz said at a function in the occupied West Bank.

Later in the day, the army said its troops had killed an "armed terrorist" who "violated the ceasefire understandings by crossing the Forward Defense Line and approaching IDF soldiers, posing an immediate threat".

Katz also said that the military had been ordered to demolish any structure or roads that were "booby-trapped" and threatened soldiers.

The army would likewise "remove the houses in the contact villages near the border that served in every respect as Hezbollah terror outposts and threatened Israeli communities", he added.

An Israeli soldier was killed in southern Lebanon on Friday -- after the 10-day ceasefire between Israel and Lebanon came into effect -- when he entered a booby-trapped building, the military reported.

Katz has repeatedly said Israel would demolish houses along the border as part of efforts to establish a security zone in southern Lebanon.

On Saturday, Israeli forces carried out demolitions in the town of Bint Jbeil, the scene of intense fighting with Hezbollah prior to the recently agreed ceasefire.

"The overarching goal of the campaign in Lebanon is the disarmament of Hezbollah and the removal of threat to northern communities, through a combination of military and diplomatic measures," Katz said.

"If the Lebanese government continues to fail to uphold its obligations -- the IDF will do so through continued military action."

Lebanon was drawn into the Middle East war in early March when the Tehran-backed Hezbollah launched rockets towards Israel in support of Iran.

Israel responded with massive strikes across Lebanon and an invasion of southern Lebanon.