They went to war together against Iran, but Donald Trump and Benjamin Netanyahu's relationship is under strain after the U.S. president reportedly called the Israeli premier "crazy."

Trump unleashed a profane tirade over the phone at Netanyahu over Israel's threats to bomb the Lebanese capital Beirut, fearing it would undermine talks with Tehran, the Axios news outlet and ABC News reported.

Lebanese state media reported an Israeli strike near Beirut on Wednesday as well as attacks on south Lebanon, ahead of a second day of talks in Washington between Israel and Lebanon.

The state-run National News Agency (NNA) reported "the targeting of a car on the Khaldeh road", referring to an area at the southern entrance to the capital.

The Lebanese delegation to the Washington peace talks with Israel "sensed Israeli and U.S. acceptance regarding a comprehensive ceasefire, and the three parties presented proposals on specific ceasefire formulas," Baabda sources said on Tuesday.

"There is seriousness and a clear effort and interest from the U.S. in reaching a comprehensive ceasefire," the sources told MTV.

Hezbollah will not accept a "partial ceasefire" with Israel, a senior official from the Iran-backed group said Tuesday, refusing to halt attacks against northern Israel in exchange for Israel sparing Beirut's southern suburbs, although they appeared to have stopped on Tuesday.

Prime Minister Nawaf Salam commented Tuesday on the resumption of Israeli-Lebanese negotiations in Washington by saying that "what remains is to consolidate a ceasefire throughout Lebanon."

The path of negotiation is "the least costly for the country, especially since wars throughout history have ended with a victor and a vanquished, or with negotiations to resolve the conflict," President Joseph Aoun said on Tuesday.

Parliament Speaker Nabih Berri praised Tuesday Iran for insisting that a ceasefire in Lebanon remains a key condition for any deal with the United States.

Iran's parliament speaker and chief negotiator Mohammad Bagher Ghalibaf had said on Monday night that he and Berri had spoken by phone.

A strike on a car on the Khardali road in south Lebanon killed a man, his son and his daughter, who were students, as he drove them back from university exams in Beirut to the southern border village Qlayaa, where some residents were still holding out despite Israeli evacuation orders.

Theodosia Karam, the daughter, had exams at the Lebanese University in Hadath and left with her father and brother after Israel threatened Beirut's southern suburbs. They drove to their hometown, Qlayaa.

Israel said Monday it would once again target Beirut's southern suburbs, a Hezbollah stronghold mostly spared heavy attacks since April, as it stages its deepest incursion into Lebanon in two decades.

The Saudi Ministry of Foreign Affairs on Monday expressed the Kingdom's condemnation of Israel's escalating attacks in Lebanon and its "categorical rejection of the Israeli incursion Lebanon's territory and the violation of its sovereignty."