Israeli soldiers have shot dead two people in southern Lebanon, the Lebanese health ministry says, in the first fatal incident reported since the latest ceasefire between Israel and the Iran-backed armed group Hezbollah appeared to take hold at the weekend.

Lebanon's state-run National News Agency said two men were killed while they were standing near a bulldozer that was unblocking a road in the town of Nabatieh al-Fawqa.

Hezbollah condemned the shooting as "a blatant violation of the ceasefire".

Israel's military said soldiers in the Ali al-Taher ridge area, just east of Nabatieh al-Fawqa, fired at "four Hezbollah terrorists riding a bulldozer and a motorcycle" who posed a threat.

It added that the group had crossed into the Israeli-declared "security zone" in southern Lebanon and ignored warning shots from the soldiers.

The Israeli military also said that, in a separate incident, soldiers struck a "cell of armed terrorists" north of the security zone. It released a photo that it said showed one of the men holding a rifle. There were no immediate reports of any casualties.

NNA identified the two men killed in Nabatieh al-Fawqa as Mohammed Amhaz and Sajed al-Hajj Ali. It said they were with a team from the Islamic Health Association, an emergency service linked to Hezbollah, and a bulldozer that was working to reopen roads and recover bodies underneath rubble in the al-Deir neighbourhood.

Hezbollah's military wing, the Islamic Resistance, said in a statement: "What the enemy has committed constitutes a blatant violation of the ceasefire, which the Resistance has adhered to up to this point". It did not say whether the group would retaliate.

The ceasefire has largely held since Sunday, marking the longest lull in weeks of escalating hostilities that spilled over from the US-Israeli war with Iran.

Israeli Prime Minister Benjamin Netanyahu said on Monday night that Israeli troops had full freedom of action against any Hezbollah threat and would remain in Lebanon "as long as is necessary".

Tuesday's deaths came as Lebanese and Israeli officials opened talks in Washington aimed at advancing what the US state department described as "a comprehensive peace and security agreement between the two countries".

Iran has insisted that Lebanon be covered by the agreement signed with the US last week, warning that violations of the ceasefire could undermine wider diplomatic efforts.

Iran's ambassador to the UN in Geneva, Ali Bahreini, warned on Tuesday that violations of the ceasefire framework risked derailing broader diplomatic progress.

"Lebanon is an unquestionable part of the agreement, and whatever happens in Lebanon affects the whole process, and it is the United States which should use all its leverage against Israel to make it stop attacks against Lebanon."

Lebanon was drawn into the war between Israel, the US and Iran on 2 March, when Hezbollah launched rockets into Israel in retaliation for a strike that killed Iran's supreme leader.

Israel responded by launching a bombing campaign across Lebanon and invading a significant part of the country's south.

Israeli attacks in Lebanon have killed at least 4,192 people since the current round of hostilities began, according to the Lebanese health ministry. More than 1.2 million people have also been displaced, Lebanese authorities say.

Israeli authorities say 36 Israeli soldiers and four civilians have been killed on both sides of the border during the conflict.