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.

The Israeli military said it intercepted two projectiles that crossed into Israeli territory from Lebanon on Wednesday, after earlier announcing the interception of a "hostile aircraft" that had also crossed into Israel.

"Following the sirens that sounded a short while ago in the area of Misgav Am, the Israeli Air Force intercepted two projectiles that crossed from Lebanon into Israeli territory," the military said, referring to a community on the northern border.

The United Nations chief has proposed three options to help end the decades-old conflict between Lebanon's Iran-backed Hezbollah militants and Israel when the 8,100-member U.N. peacekeeping mission in southern Lebanon ends on Dec. 31.

All of the options presented to the U.N. Security Council by Secretary-General Antonio Guterres would continue U.N. military monitoring of the boundary between Israel and Lebanon, support Lebanese forces in deploying throughout the country and strengthen political efforts to end the fighting, which has persisted despite a nominal ceasefire.

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.

Israeli Prime Minister Benjamin Netanyahu announced on Tuesday allocations of 13 billion shekels (more than $4.5 billion) to secure and develop northern communities along the Lebanon border, battered by weeks of fire from Iran-backed Hezbollah.

"The government made dramatic decisions today to strengthen the north. We are investing more than 13 billion shekels today, in addition to the seven billion we have already provided -- a total of 20 billion shekels going to the communities of the north," Netanyahu said following the government's approval of the measure.

Israeli strikes on southern Lebanon on Tuesday killed five people, including a child, and wounded 48, the Lebanese health ministry said.

Those wounded in the strikes across the south included "a doctor and five employees of Tebnine Governmental Hospital, which sustained damage in yet another episode of the series of attacks carried out by the Israeli enemy against hospitals and health centers", the ministry said in a statement.

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.

Israel and Lebanon could reach a peace agreement within days were it not for the obstacle posed by Hezbollah, U.S. Secretary of State Marco Rubio said Tuesday, as the two sides began a fourth round of talks in Washington.

"Israel and Lebanon can do a peace deal tomorrow," Rubio told the Senate Foreign Relations Committee.

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.

In a south Lebanon hospital heavily damaged by deadly Israeli strikes nearby, Dr Nasser al-Masri held a new-born baby, calling him "a message of life and hope" despite the war.