Hezbollah said it carried out a "defensive warning strike" on an Israeli military position in the disputed Shebaa Farms area on Monday, citing repeated Israeli ceasefire violations including airstrikes and shelling in Lebanon.
The Israeli military said Hezbollah launched two missiles but caused no casualties.
Israeli Prime Minister Benjamin Netanyahu said on Monday that Israel would respond "strongly" to the strike.
Earlier, Lebanon's state-run National News Agency (NNA) reported that Israeli forces fired two artillery shells towards the southern Lebanese town of Beit Lif in the Bint Jbeil district, while heavy machine gun fire targeted Yaroun.
No injuries were reported in either incident, NNA said, but a separate Israeli strike injured others in the town of Talousa.
Lebanese authorities also said Israeli strikes on southern Lebanon killed at least two people on Monday as the ceasefire, which follows more than a year of hostilities between Israel and Lebanese armed group Hezbollah, appeared increasingly fragile.
Lebanon has accused Israel of committing at least 50 violations of the ceasefire.
The truce, which came into effect early on Nov. 27, stipulates that Israel will not carry out offensive military operations against civilian, military or other state targets in Lebanon, while Lebanon will prevent any armed groups, including Hezbollah, from carrying out operations against Israel.
Lebanon and Israel have already traded accusations of breaches, and on Monday Lebanon said the violations had turned deadly.
One person was killed in an Israeli air attack on the southern Lebanese town of Marjayoun, about 10 km (6 miles) from Israel's northern border, Lebanon's health ministry said.
Lebanon's state security said an Israeli drone strike had killed a member of its force while he was on duty in Nabatieh, 12 km from the border. State security called it a "flagrant violation" of the truce.
The Lebanese army said an Israeli drone hit an army bulldozer in northeast Lebanon near the border with Syria, wounding one soldier.
The Israeli military did not immediately respond to questions about the incidents in Marjayoun and Nabatieh.
It issued a statement saying it had attacked military vehicles operating near Hezbollah military infrastructure in Lebanon's Bekaa Valley and military vehicles near the border with Syria.
The Israeli military acknowledged that a Lebanese soldier was wounded in one of its attacks and said the incident was under review.
Lebanon's parliament speaker, Nabih Berri, an ally of Hezbollah and Beirut's main interlocutor in the ceasefire talks, said Lebanon had logged at least 54 Israeli violations so far.
In a statement issued by his office, Berri urged the committee tasked with monitoring the ceasefire to "urgently" begin work, and to "oblige" Israel to halt its violations and withdraw troops from Lebanese land.
The ceasefire deal stipulates that a monitoring mechanism hosted by the United Nations peacekeeping force in Lebanon and chaired by the United States would "monitor, verify and assist in ensuring enforcement" of the ceasefire.
Israeli Foreign Minister Gideon Saar denied that his country had breached the accord, saying the problem lay with Hezbollah moving weapons and crossing south of the Litani river, in defiance of last week's deal.
"Israel is committed to the successful implementation of the ceasefire, but we will not accept a return to the situation as it stood on October 6, 2023. If violations occur, Israel will enforce (the pact)," he said in a statement.
Public broadcaster Kan and other Israeli media outlets reported on Monday that US envoy Amos Hochstein, who brokered the ceasefire after weeks of shuttle diplomacy, had warned Israel against alleged violations.
Israeli Finance Minister Bezalel Smotrich said Monday that Israel must deal Hezbollah a "powerful blow" after he said it made a "big mistake" by firing at Israeli territory.
