Amos Hochstein, a top U.S. envoy to the Middle East, arrived in Beirut, the Lebanese capital, on Tuesday as efforts to broker a cease-fire between Israel and Hezbollah appeared to be intensifying.

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.

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 the movement has a strong presence, possibly to stir anti-Hezbollah sentiment.