Attacks come on the day Israeli troops were supposed to withdraw from southern Lebanon and allow people to return home.
Israel has killed at least four people, including a Lebanese soldier, in south Lebanon on the day Israeli forces were due to withdraw under a ceasefire deal.
At least 32 civilians were wounded on Sunday as Israeli forces opened fire in at least two border towns on “citizens who were trying to return to their villages,” Lebanon’s Ministry of Public Health on said.
Israeli fire killed a Lebanese soldier and wounded another in Mais al-Jabal village, according to a statement by the Lebanese army.
Israeli military spokesman Avichay Adraee issued a message earlier on Sunday to residents of more than 60 villages in south Lebanon, telling them not to return.
The Israeli killings violate a ceasefire agreement reached in November, under which its forces were supposed to withdraw from Lebanon at 02:00 GMT on Sunday.
Israeli Prime Minister Benjamin Netanyahu blamed Lebanon for the delay, saying Hezbollah has not pulled back sufficiently from the border region. Lebanon denies the claim and has urged Israel to respect the deadline.
Al Jazeera correspondent Zeina Khodr, reporting from Borj al-Mlouk in southern Lebanon, said the Israeli military claims it needs to stay longer because the Lebanese army is not doing its job to ensure Hezbollah is disarmed and its military infrastructure dismantled.
“The Israelis are saying there are not enough Lebanese troops on the ground and allege Hezbollah is still here. There is no independent confirmation concerning those claims,” she said.
“People here have been displaced from their homes for more than a year. They believe the Israeli military should have withdrawn in line with the ceasefire agreement. The 60-day deadline has passed.”
Under the terms of the truce, the Lebanese army was to deploy alongside the United Nations peacekeepers in the south as the Israeli army withdrew from the area over the 60-day period.
Hezbollah agreed to pull back its forces north of the Litani River, about 30km (19 miles) from the border, and dismantle any remaining military infrastructure in the south.
The deal, brokered by the United States and France in November, ended more than a year of fighting triggered by Israel’s war on Gaza.
Lebanon parliament’s Speaker Nabih Berri, whose Amal Movement party is allied with Hezbollah, said in a statement that Sunday’s bloodshed “is a clear and urgent call for the international community to act immediately and compel Israel to withdraw from occupied Lebanese territories”.
Berri had served as a mediator between the group and the US during ceasefire negotiations.
Meanwhile, in a joint statement, the UN envoy in Lebanon and the chief of the UN peacekeeping mission to Lebanon (UNIFIL) said conditions are “not yet in place” for the safe return of Lebanese citizens to southern Lebanon.
They said the timelines set under the ceasefire deal were not met, urging recommitment from both Israel and Lebanon.
“People are frustrated,” said Al Jazeera’s Khodr. “They are saying the Lebanese army cannot protect us; it’s standing in the middle.”