"The overarching goal of the campaign in Lebanon is to disarm Hezbollah and remove the threat to the northern communities (of Israel), through a combination of military and diplomatic measures," Katz said during a ceremony marking Israel's national day of remembrance for fallen soldiers and victims of terror.

"We will act in the same way with regard to high-trajectory fire (towards Israel) from north of the Litani and from throughout Lebanon", he added, referring to the Litani river, a natural marker that cuts across southern Lebanon, below which Israel wants no more Hezbollah presence.

Though a truce between Israel and Lebanon took effect Friday, Israeli troops are still present and actively fighting Hezbollah militants in Lebanon's south, with Katz saying Sunday that troops would use "full force" if threatened.

Israel has conducted airstrikes across Lebanon and invaded the country's south after Hezbollah entered the Middle East war in support of its backer Iran on March 2.

An Arabic-language spokesperson for Israel's military on Monday warned Lebanese residents of the country's south not to return to the homes it had earlier urged them to evacuate, saying it considered Hezbollah activities in the area to be ceasefire violations.

Israel and Lebanon are still engaged in talks under US mediation to prolong the current truce.

The two-week ceasefire between the US and Iran looms in the background of talks, with the truce set to expire overnight Tuesday with no new deal yet struck.