Lebanon and Hezbollah have agreed to a U.S. proposal for a ceasefire with Israel with some comments on the content, a top Lebanese official told Reuters on Monday, describing the effort as the most serious yet to end to the fighting.

Amos Hochstein is expected in Beirut on Tuesday, according to two Lebanese official sources, in a sign of progress in ceasefire negotiations for the deadly cross-border conflict between Israel and Hezbollah in Lebanon.

Lebanon and the Hezbollah militia have reached agreement on a US plan for a cease-fire with Israel, Reuters reported on Monday.

An airstrike killed five people in central Beirut, and rockets fired from Lebanon killed one person in northern Israel and caused several injuries in a Tel Aviv suburb, amid a continuing U.S. push for a cease-fire deal between Israel and Hezbollah militants.

An Israeli airstrike killed four people in a central Beirut neighbourhood on Monday, Lebanon's health ministry said, the second day in a row Israel has hit a target within the capital as it presses it campaign against the Iran-backed Hezbollah.