Lebanon's state-run National News Agency (NNA) reported intermittent artillery shelling in the country's south on Monday but no airstrikes -- a lower level of violence compared to previous days.

Hezbollah has not commented on the agreement, but the Iran-backed group has not claimed any fresh attacks on Monday on Israeli targets.

"Lebanon was not informed of the terms of the agreement or the time of the ceasefire," the source said on condition of anonymity.

Few details have been made public about the agreement announced overnight.

Lebanese parliament speaker Nabih Berri, a Hezbollah ally who acts as an intermediary between the group and the US, praised the deal, thanking the United States and Tehran for their "insistence on including... an essential and binding clause on halting the Israeli aggression on all of Lebanon".

Israel and Hezbollah have been at war since March 2 when the Iran-backed group fired rockets at Israel to avenge the killing of Iran's supreme leader in US-Israeli strikes days earlier.

Israel responded with a campaign of airstrikes and a ground invasion. Previous ceasefire announcements have failed to stop the fighting.

Pakistan's Prime Minister Shebhaz Sharif, whose country has been mediating between Tehran and Washington, said that "both sides have declared the immediate and permanent termination of military operations on all fronts, including in Lebanon".

Iran's Deputy Foreign Minister Kazem Gharibabadi said that "a permanent and immediate end to the war has been declared on all fronts, including Lebanon".

AFP correspondents on Monday reported a cautious return of some residents to their homes in areas of south Lebanon not occupied by Israel's army.