U.S. envoy Amos Hochstein said he will travel to Israel on Wednesday to try to secure a ceasefire ending the war with Lebanon's Hezbollah group after declaring additional progress in talks in Beirut.

Hochstein arrived in Beirut on Tuesday, seeking to clinch a ceasefire agreement after the Lebanese government and Hezbollah agreed to a U.S. ceasefire proposal, although with some comments.

"The meeting today built on the meeting yesterday, and made additional progress," Hochstein said after his second meeting with Parliament Speaker Nabih Berri, endorsed by the heavily armed, Iran-backed Hezbollah to negotiate.