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.

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.

The Lebanese, Arab and international contacts that managed to avert an Israeli strike on Dahieh on Monday will contribute to a better atmosphere in today's talks between Israel and Lebanom in Washington, Baabda sources said on Tuesday.

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.

Ceasefires have been announced, often to great fanfare, in Gaza, Lebanon and Iran. So why is there still so much fighting?

In just the last few weeks, Israeli forces have captured more territory in Gaza and killed two top Hamas militants there, as well as more than a dozen other people. In Lebanon, Israeli troops captured a Crusader fortress over the weekend in their deepest incursion in 26 years, as Hezbollah kept up rocket fire into northern Israel.