A senior Hezbollah official told AFP on Monday that the Iran-backed group has had "no direct contact" with President Donald Trump, despite recent statements from the US leader suggesting otherwise.

Washington considers Hezbollah a "terrorist" group, including both its military and political wings, and recently imposed sanctions on several of its lawmakers.

Lebanese Information Minister Paul Morcos said Monday that 29 Lebanese army members have been killed in Israeli strikes since March, two days after an Israeli airstrike on a vehicle in southern Lebanon killed three members of the Lebanese army, including a brigadier general and a captain.

Morcos said that since the Israel-Hezbollah war began on March 2, three police, one member of the General Security Directorate and 13 state security members have been killed in Israeli attacks. Also killed was a member of the parliament’s security.

The Iranian military's joint command said Monday it was halting its offensive operations, after Israel and Iran exchanged fire in their first attacks since the U.S. struck a ceasefire with Tehran two months ago.

Iran had delivered a "painful response" to Israel and "accordingly, the cessation of armed forces operations is hereby announced", the Khatam al-Anbiya command said in a statement carried by state television.

Israeli bombardment has damaged a World Heritage site in the southern city of Tyre, a culture ministry official told AFP on Monday, as correspondents there saw debris and damage.

One of the oldest cities on the Mediterranean coast, Tyre lies around 20 kilometers from the Israeli border, and its UNESCO World Heritage listed ruins are located in two main areas of the city.

U.S. Ambassador Michel Issa met Monday with President Joseph Aoun, as Israel and Iran traded fire after Israel's bombing of Beirut's southern suburb.

Issa said the U.S. places great importance on Lebanon and has decided that Sunday's events must not expand further. "What happened yesterday is a political message, and we in the United States have decided that the confrontation must not expand any further," Issa said after meeting Aoun.

Israeli strikes targeted overnight into Monday Habboush, Srifa, Zefta, Yater, Nabatieh, Safad al-Battikh, Sojod, Jabal Safi, al-Mansouri, Ainqana, Qalaway, al-Sharqiyeh and al-Hallousieh, as Israel and Iran exchanged attacks over Israel's bombing of Dahieh.

Four people were killed in the strike on Zefta, the national News Agency said, adding that several others were killed in Srifa.

The Israeli military has vowed to press ahead with its military campaign in Lebanon and said it would step up operations against Hezbollah.

"The (Iranian) regime is attempting to establish a new equation through direct attacks on Israeli territory in response to IDF operations in Dahieh," military spokesman Brigadier General Effie Defrin said Sunday, in a televised statement.

Iran, Hezbollah, and others have repeatedly dragged both Israel and Lebanon into "pointless and destructive conflicts" and "Hezbollah has a simple choice: it can continue fighting a pointless war, or it can finally allow the return of the displaced and the reconstruction of Lebanon," a U.S. official said on Sunday.

In remark to U.S. news portal Axios, the official claimed "the terms on the table are fair, have the consent of both sovereign governments, and provide a clear path to end the fighting."

The Israeli military said Sunday it uncovered a sprawling tunnel network beneath the Beaufort castle in southern Lebanon, saying it was built to give Hezbollah a fortified strike hub just kilometers from Israeli territory.

Israeli soldiers recaptured the crusader-era castle recently, giving the military a strategic toehold it once occupied for nearly two decades.

Iran threatened to retaliate against the United States and Israel for fresh strikes in Beirut's southern suburbs on Sunday, further dampening hopes for a lasting peace as the Middle East war reached its 100th day.