Israel's prime minister, defence minister and military chief have stated the military would continue to act to "neutralise" threats against Israeli soldiers and citizens.
In a joint statement issued after a security discussion, the officials clarified that it includes demolishing infrastructure and maintaining the security zone in southern Lebanon.
The statement added that the three officials "made it clear that the security of Israeli citizens and IDF forces will remain their guiding principle without compromise".
Israel was not a party to the peace agreement between the US and Iran, and says it will not withdraw its troops from Lebanon, but on Friday it agreed a new ceasefire.
Though intense fighting continued for another day, Lebanese officials said it had abated since Saturday night.
Israel and Lebanon were due to start a new round of talks in Washington on Tuesday, with Beirut determined to press ahead with direct negotiations even as they appear to be overshadowed by Iran's decision to make Lebanon part of its negotiations with the United States.
Hassan Wazni, director of a hospital in the heavily bombarded city of Nabatieh, said it was the first two full days of calm since the war began.
"I'm monitoring the situation day by day, and most of the time I'm sleeping in the hospital. This is the longest a ceasefire has held," he told Reuters by phone.
More than a million Lebanese have been displaced by the war, and though some have begun returning to their homes, many are still too wary.
In Qennarit, a southern town, mourners carried the bodies of four women killed in Saturday's wave of Israeli strikes.

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