Two projectiles hit a container vessel in the Gulf as it was leaving port in Iraq, a Swiss-based company said Tuesday, after Iran's Revolutionary Guards said they had targeted the ship.

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.

Israel continued to strike southern Lebanon on Tuesday as Iran-backed Hezbollah attacked its troops there despite an apparent Washington-brokered de-escalation deal and a fourth round of U.S.-hosted talks between Lebanon and Israel.

The ambassadors of Israel and Lebanon began a new round of direct talks in Washington on Tuesday after U.S. President Donald Trump said he had received commitments from both sides to de-escalate.

Lebanon's health ministry said Tuesday that Israeli strikes a day earlier near a hospital in the southern city of Tyre killed four people and wounded 127 others, including 39 staff from the facility.

The ministry statement said the wounded staff at the Jabal Amel hospital were "four doctors, 27 nurses, and eight (administrative) employees -- four of whom are in critical condition and receiving treatment in intensive care".

Israel's defense minister said Tuesday Washington had given its backing to potential Israeli strikes on Beirut's southern Dahieh suburb if the Iran-backed group attacked northern Israeli communities.

"The Prime Minister and I led a coordinated move together with the IDF to establish a new equation... If Israeli towns continue to be attacked, we will evacuate and strike the Shiite Dahieh quarter in Beirut, Hezbollah's stronghold," Israel Katz said at a conference, a defense ministry statement said.

Lebanon's public university said on Tuesday it was postponing some examinations after two students and their father were killed while returning to south Lebanon after sitting exams a day earlier.

The state-run National News Agency (NNA) said a dentist from the border village of Qlayaa "was killed with his son and daughter when an enemy drone targeted his car on the Nabatieh-Khardali road" on Monday.

Israel has portrayed the capture of a Crusader-era fortress as a turning point in its offensive against Hezbollah, but the operation has also sparked fears of a new quagmire in south Lebanon.

Israeli authorities praised the symbolism of the capture of Beaufort, perched atop a rocky outcrop, as they announced its capture in an assault documented by military drones.