Israel will continue its operations in southern Lebanon for now and Lebanese residents forced from their homes by Israel will not be able to return, Defense Minister Israel Katz said, Reuters reported.
His comments came a day after Lebanon and Israel said they had agreed to implement a truce during talks in Washington.
The deal is contingent on a ceasefire by the militant group "Hezbollah".
In a statement, Katz said troops would remain in a so-called security zone in southern Lebanon, including in the Beaufort Castle area – A 900-year-old fortress that Israel captured on Saturday.
He said Israel would continue to "destroy the terrorist infrastructure in the area", with Israel having "freedom of action, supported by the United States, to strike Beirut in response to attacks on Israeli settlements and territory".
Lebanon and Israel agreed yesterday on a new, US-backed ceasefire in Lebanon. They had previously agreed to a ceasefire in April, which was then extended in May, but violence has continued.
Israeli National Security Minister Itamar Ben-Gvir criticized the agreement between Israel and Lebanon for a new attempt at a ceasefire as a "serious mistake", DPA reported.
In a post on the "Ex" platform he described it as "unrealistic dreams of advisers who are pushing the prime minister to make wrong decisions".
The agreement will actually only strengthen the Iranian-backed Lebanese militia "Hezbollah", Ben-Gwir said. "In practice, "Hezbollah" will only become stronger, and instead of defeating it, Israel is resigning itself to its very existence," he wrote.
Ben-Gwir added that the Lebanese state is "a partner of "Hezbollah"" and is unable to push the militia, which is hostile to Israel, out of the border area.
The minister is the leader of the far-right Israeli party "Jewish Power", which is part of Prime Minister Benjamin Netanyahu's coalition.