Hezbollah thanked its backer Iran on Monday for insisting that Lebanon, where Israel and the militants have been at war, be included in the deal to end the Middle East conflict.

"Hezbollah expresses its profound gratitude" to Iran's leaders, forces and people "for their steadfast support of Lebanon, its people and its resistance, and for their insistence that Lebanon be included in any understanding leading to the cessation of war", the group said in a statement.

Iran's foreign ministry on Monday said the United States must ensure that Israel commits to stopping the war in Lebanon under a framework deal to end the Middle East war.

"The United States must honor its commitments. It must ensure that the Zionist regime also respects its own regarding Lebanon," said foreign ministry spokesman Esmaeil Baqaei in a press briefing, adding that Tehran "neither trusts Israel nor the United States".

A Hezbollah official told Reuters ​on Monday that ‌the group has not carried out any ​operations since the ​Iran-U.S. deal was announced ⁠and that its ​position on the ceasefire ​was linked to Israel's adherence to it.

The deal between the United States and Iran to end their war, negotiated in secret and still not revealed in detail, was greeted with skepticism but a measure of relief among ordinary people across the Middle East.

In Lebanon, AFP saw displaced people preparing to return to homes they fled in the south of the country, despite Israeli ministers declaring that they do not feel bound by the agreement to halt their own offensive against Hezbollah.

An Israeli drone targeted Monday a car in the southern town of Kfartebnit near the Israeli-designated "Yellow Line", where Israeli troops remain despite the announcement of a U.S.-Iran deal.

The strike killed the car's driver. Another drone strike on a car earlier in the day had wounded several people in the same town.

The army on Monday urged displaced residents to delay their return to southern border villages, hours after an agreement was announced between Washington and Tehran to end the Middle East war, including in Lebanon.

"The army command emphasizes the need for residents to delay returning to southern border villages and towns, and to adhere to instructions of the deployed army units, in order to safeguard their safety from the risk of Israeli violations and attacks," a statement said.

Israeli figures across the political spectrum on Monday slammed the deal between the United States and Iran to end the Middle East war, including in Lebanon, saying it would not protect their country's security.

Two far-right ministers insisted Israel was not bound by the deal, while a leading opposition contender in upcoming elections said it marked a "dangerous turn" for the country's security.

Prime Minister Benjamin Netanyahu has told U.S. President Donald Trump that Israel will not withdraw from its current positions in Lebanon and does not consider itself bound by the Lebanese clause in the emerging U.S.-Iran agreement, Israeli media reported Monday.

During a phone conversation last night, Netanyahu informed Trump that Israel intends to continue its military operations against Hezbollah and will not accept any limitations on its freedom of action. According to reports, the prime minister received unanimous backing from his cabinet for this stance.

President Joseph Aoun on Monday expressed hope that a deal between Washington and Tehran to end the Middle East war would put a "definitive end" to the conflict between Israel and Hezbollah.

In a statement issued by his office, Aoun praised the memorandum's affirmation that "Lebanon's security and safety are an integral part of any effort to consolidate stability in the region".

Parliament Speaker Nabih Berri, a Hezbollah ally who acts as an intermediary between the group and the U.S., praised Monday an agreement between the United States and Iran to end the Middle East war on all fronts.

Berri thanked the United States and Tehran for their "insistence on including... an essential and binding clause on halting the Israeli aggression on all of Lebanon".