At least two people were killed on Monday in Israeli strikes on southern Lebanon, Lebanese authorities said, as a ceasefire ending more than a year of hostilities between Israel and Lebanese armed group Hezbollah appeared increasingly fragile.

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 kilometres from the border with Israel, 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 from Reuters 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.

At least 54 Israeli truce violations so far: Lebanon

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 (UNIFIL) and chaired by the United States would "monitor, verify and assist in ensuring enforcement" of the ceasefire.

"The aggressive actions carried out by the Israeli occupation forces constitute a flagrant violation of the terms of the ceasefire agreement," Berri said.

WATCH | Israel-Hezbollah ceasefire appeared to be holding last week: 

Ceasefire brings some calm to Israel, Lebanon border

A ceasefire between Israel and Hezbollah appears to be holding in Lebanon, bringing some calm to the region, after more than a year of fighting. It’s also allowed thousands of displaced Lebanese civilians to flee for home, despite warnings from the Israeli military to hold off.

Public broadcaster Kan and other Israeli media outlets reported on Monday that U.S. envoy Amos Hochstein, who brokered the ceasefire after weeks of shuttle diplomacy, had warned Israel against alleged violations.

The Israeli government did not immediately comment on the reports.