Israel has killed two people, including a State Security officer, in separate attacks in Lebanon as it continues its assaults on the country since the ceasefire with Hezbollah came into effect last week.

For its part, the Lebanese group said on Monday that it carried out a “preliminary defensive response” to the “repeated violations” of the ceasefire by attacking an Israeli military base in the hills of Kfar Chouba, a disputed area that Lebanon claims as its own.

Hezbollah said Israeli breaches of the truce that went into effect on Wednesday include deadly air raids across Lebanon, shooting at civilians in the south, and flying drones and jets in Lebanese airspace, including over the capital, Beirut.

The group said it launched its “warning” attack because “appeals by the relevant authorities to stop these violations did not succeed”.

The renewed violence highlights the fragility of the ceasefire, which ended a devastating war that killed nearly 4,000 people in Lebanon and saw Hezbollah fire rockets daily at Israel.

Earlier on Monday, Lebanon’s State Security agency said an Israeli rocket killed officer Mahdi Khreis in the southern district of Nabatieh, calling the incident a “blatant violation” of the ceasefire and a dangerous escalation.

Israeli bombardment in neighbouring Marjayoun killed another person, Lebanon’s Ministry of Public Health said. A drone attack in the northeast of the country also injured a Lebanese soldier.

Although the ceasefire calls on all parties to hold their fire, Israel has been launching near-daily attacks against Lebanon.

Lebanese media have also reported that the Israeli military is using the truce to advance into new neighbourhoods in towns that it had entered during the war.

After months of low-level hostilities, Israel launched an all-out war on Lebanon on September 23 with the stated aim of defeating Hezbollah.

The Lebanese group had been targeting Israeli military bases in northern Israel for months in an effort that it said was aimed at pressuring Israel to end its war on Gaza.

Israel assassinated top Hezbollah military and political leaders early in the war, including the group’s chief Hassan Nasrallah.

It also levelled thousands of buildings and homes across Lebanon with its focus on southern and eastern Lebanon and the Beirut suburbs of Dahiyeh – areas where Hezbollah is popular.

Still, Hezbollah continued to fire rockets at northern and central Israel. The group also said it inflicted heavy losses on invading Israeli troops that crossed into the country.

The truce, which was brokered by the United States and France, stipulates that the Israeli military must withdraw from Lebanon within 60 days and Hezbollah must move away from the border with Israel until it is north of the Litani River.

During those two months, the Lebanese army is to deploy to southern Lebanon to be the only armed force there.

Although Israel said its recent attacks are to “enforce” the truce, the agreement prohibits attacks by all sides.

Lebanese Parliament Speaker Nabih Berri, a Hezbollah ally who was Lebanon’s chief negotiator in the ceasefire talks, stressed on Monday that Israel has violated the truce more than 54 times, including by carrying out air raids and demolishing homes near the border.

“All these activities represent flagrant violations of the ceasefire agreement,” he said in a statement.

On Monday, Israeli Defence Minister Israel Katz suggested the country is ready for further escalation, promising a “harsh response” to the Hezbollah attack.

“We promised to act against any violation of the ceasefire by Hezbollah – and that is exactly what we will do,” he said in a social media post.

But the US voiced confidence in the truce agreement on Monday. “Broadly speaking, it has been successful in stopping the fighting and getting us on a path where we are not seeing the daily loss of life that we had seen for two months prior,” State Department spokesperson Matthew Miller told reporters.

He said the US administration will work through a monitoring mechanism established by the agreement to address potential violations to the ceasefire.