United States envoy Amos Hochstein is due to visit the Lebanese capital Beirut “imminently” after Lebanon responded “positively” to a US-backed proposal to stop the Israel-Hezbollah war, Lebanese Prime Minister Najib Mikati said on Monday.

Hezbollah, a heavily armed movement backed by Iran, endorsed its long-time ally Parliament Speaker Nabih Berri to negotiate over a ceasefire.

Local reporting suggested that Hezbollah had approached the US-backed deal with “openness” even as Israeli strikes in Lebanon have intensified.

Israel has stepped up its air attacks on Lebanon’s south, where it is also conducting a ground invasion, the eastern Bekaa Valley and Beirut. In the capital, it has carried out multiple strikes on the southern suburbs, known as Dahieh, where Hezbollah is based.

The U.S. official overseeing contacts to secure a ceasefire between Israel and the Iran-backed Hezbollah in Lebanon is due to visit Beirut on Tuesday, sources in Lebanon said on Monday, with Beirut expected give its response to a U.

Israeli troops are understood to have made their deepest incursion into southern Lebanese territory since the recent offensive began on October 1, as the militant group Hezbollah considered its response to a fresh ceasefire proposal.

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.