According to Lebanon's embassy in Washington, the agreement, which would not end the conflict in that country, calls for Israel to refrain from strikes on Beirut and its suburbs controlled by Hezbollah, while the Iran-aligned group would halt its attacks on Israel.
Hostilities in southern Lebanon continued on Monday evening.
US President Donald Trump said Israel and Hezbollah in Lebanon agreed to halt their attacks on each other for the time being.
Trump also said Israel would not send troops into Beirut, despite earlier threats to do so.
He also said Israeli Prime Minister Benjamin Netanyahu agreed to pull back any troops preparing to attack Lebanon.
After Trump's announcement, Netanyahu said Israel would continue military operations in southern Lebanon, where ground forces are pushing toward the Zaharani River, their deepest incursion in Lebanon in 25 years.
Hezbollah lawmaker Hassan Fadlallah said the militia would support a full ceasefire across all Lebanon as a precursor to the withdrawal of Israeli troops. He did not say whether the group would stop its strikes on Israeli territory.
The halt to Israeli attacks on Hezbollah applies to the southern suburbs of Beirut, Lebanese President Joseph Aoun said.
"Under the proposed arrangement, Israeli strikes on Beirut's southern suburbs would cease in exchange for Hezbollah refraining from carrying out attacks against Israel," the Lebanese presidency said in a statement posted on X.
Lebanon said it would seek to expand the ceasefire in talks with Israel in Washington on Wednesday. That could clear the path for renewed efforts to end the three-month-old war between the US and Iran, which has been stuck in limbo for weeks under a fragile ceasefire as negotiators have been unable to agree on an initial framework for peace talks.
The Israel-Hezbollah war erupted on March 2 as an offshoot of the broader conflict and has been entangled with it ever since.
Iran has insisted on a halt to Israeli attacks in Lebanon as a condition of any deal to end the war, while the United States has said the two conflicts are separate.
Iranian state media said earlier Tehran was halting indirect negotiations with the US and might end a ceasefire that has largely held since early April, citing the war in Lebanon.
There was no direct confirmation of the reports from Iranian officials, and Trump told an NBC reporter that he had not heard from Iran.
Since mid-March, Trump has repeatedly said he is close to signing a peace deal but has yet to do so. Despite the ceasefire, Iran and the United States have exchanged strikes several times over the past week.
Meanwhile, the head of Iran's Revolutionary Guards Quds Force, Esmaeil Qaani, threatened to expand its blockade of the Strait of Hormuz to the Bab El Mandeb Strait, another chokepoint at the mouth of the Red Sea.
Iran has already bottled up maritime traffic in the Gulf that before the war provided one-fifth of the world's oil and liquefied natural gas, sending prices sharply higher.
with DPA
