The U.S.-Iran agreement to conclude the Middle East war is a significant strategic setback for Israel and underscores its waning influence in Washington, Israeli analysts said.

Although the accord, announced by Pakistan early Monday, remains incomplete and is expected to be finalized within 60 days, its preliminary framework has already raised concern in Israel.

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 said on Monday that Tehran still holds "deep mistrust" of the United States despite an agreed framework aimed at ending the war.

"Unfortunately, it must be acknowledged that Iran's deep mistrust of the United States stems from long history of wrongdoing by American leaders," said foreign ministry spokesman Esmaeil Baqaei in a weekly press briefing.

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".

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.

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.

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".

Lebanon has not been informed of details of an agreement between the United States and Iran to end the Middle East war on all fronts including in Lebanon, an official source told AFP on Monday.

Lebanon's state-run National News Agency (NNA) reported intermittent artillery shelling in the country's south on Monday but no airstrikes -- a lower level of violence compared to previous days.

The United States and Iran are to hold indirect meetings in Doha this week ahead of the formal signing of a deal aimed at ending the Middle East war, a diplomat told AFP on Monday.

"Separate preparatory meetings with each side will now take place in Doha this week, ahead of the official signing in Switzerland and the start of the technical talks," the diplomat said, speaking on condition of anonymity to discuss the sensitive arrangements.