Israeli troops were demolishing Tuesday houses, schools and buildings in the southern border towns of Khiam, Bint Jbeil, Beit Leef, Shamaa, al-Bayyada and Naqoura, in an area in south Lebanon below what Israel called the "Yellow Line".
The Israeli military also dropped thermal balloons overnight over border villages.
A ceasefire agreed between Israel and Lebanon was announced on Friday and included Hezbollah, whose rocket fire in support of Iran drew Lebanon into the war.
Israeli attacks on Lebanon have killed at least 2,387 people since the war with Hezbollah erupted six weeks ago, a Lebanese government body said in a new toll.
The disaster risk management unit added that 7,602 people had been wounded over the same period.
Since the 10-day ceasefire went into force on Friday, authorities and rescuers have been recovering bodies under the rubble of buildings in areas that were subjected to heavy Israeli strikes.
Israel and Lebanon, which have no diplomatic relations, will hold a second round of talks in Washington on Thursday, a State Department official told AFP.
Sporadic violence continued and Israel's military warned civilians against returning to dozens of villages in southern Lebanon, claiming Hezbollah's activities were violating the truce.
The U.N. Security Council condemned on Monday the killing of a French peacekeeper in Lebanon, whose death Paris blamed on Hezbollah.
The Frenchman was killed and three others wounded when their unit was ambushed on Saturday as it headed to a U.N. Interim Force in Lebanon (UNIFIL) outpost cut off from the fighting between Hezbollah and Israel.
Hezbollah lawmaker Hassan Fadlallah told AFP that his group would work to break the "Yellow Line" that Israel has established in the south, even as he said it wanted "the ceasefire to continue".
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