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.

In Lebanon, the recent attacks are seen as part of Israel’s strategy to force Hezbollah and Lebanon to agree to a ceasefire, and an indication that it is prepared to expand its offensive by killing non-military members of the group and striking places outside areas where it has a strong presence, possibly to stir anti-Hezbollah sentiment.