Israel's military on Saturday issued a new warning for residents of nine southern villages to evacuate.
Israel and Lebanon's militant Hezbollah group have kept up their attacks despite a ceasefire in place since April 17.
In the border village of Yaroun, Israel's military used bulldozers to destroy parts of a Catholic convent that had been empty as a result of the latest fighting.
"What we heard is that it was destroyed with bulldozers," said Gladys Sabbagh, the superior general of the Basilian Salvatorian Sisters.
Sabbagh told The Associated Press that the convent included a school that had been closed since the 2006 Israel-Hezbollah war, as well as a clinic that was recently moved to the nearby village of Rmeich.
She described the convent as a small compound housing just two nuns, who left because of the war.
Sabbagh did not have further details as Yaroun's residents have been displaced.
The Israeli military issued a statement saying that as the army was destroying Hezbollah infrastructure in Yaroun, a house that had no religious signs was damaged.
It added that as soon as the military knew it was linked to a church, soldiers "prevented any further damage from being done".
The military added that Hezbollah used the compound in the past to fire rockets toward Israel on several occasions.
It added that the military does not strike religious institutions intentionally.
The Catholic Church in Lebanon rejected claims that the compound was used for military purposes.
"We are against all (attacks on) places of worship and churches. These are places to spread peace, love and education," said Reverend Abdo Abou Kassm, director of the Catholic Centre for Information.
"These are not military bases."
The demolition at the convent came days after images of an Israeli soldier wielding an axe against the fallen statue of Jesus on the cross in the southern Lebanese village of Debel had sparked widespread condemnation, in Lebanon and internationally.
Israel says it's targeting Hezbollah infrastructure and members
In other parts of southern Lebanon, Israeli air strikes and Hezbollah attacks continued.
Lebanon's state-run National News Agency reported an air strike on a car in the village of Kfar Dajal killed two people, while another hit a home in the village of Lwaizeh, killing three.
Two others were killed in a strike on the village of Shoukin, it said.
Israel's military Arabic-language spokesperson, Lieutenant Colonel Ella Waweya, posted on X that the Israeli air force carried out about 50 air strikes over the past 24 hours targeting Hezbollah infrastructure and members.
Hezbollah said that it attacked with a drone Israeli troops who gathered on Saturday inside a house in the coastal village of Bayed.
Over the past weeks, the Israeli army has been levelling neighbourhoods in towns and villages near the Lebanese-Israeli border.
The military says it destroys buildings that were used as outposts by the Iran-backed group.
The Israeli military released a new video that it said shows Hezbollah positions in southern Lebanon being blown up.
The video, released Friday, shows soldiers holding an Israeli flag and walking among the destruction of a soccer stadium in the Lebanese town of Bint Jbeil.
The military said on its website that the air force "destroyed the town's stadium after it was discovered to be booby-trapped."
The latest war between Israel and Hezbollah began on March 2, when Hezbollah fired rockets into northern Israel, two days after the United States and Israel launched a war on its main backer, Iran.
Israel has since carried out hundreds of air strikes and launched a ground invasion of southern Lebanon, capturing dozens of towns and villages along the border.
