U.S. envoy Amos Hoschtein said Tuesday "a real opportunity" to end the Israel-Hezbollah conflict is "now within our grasp," but both parties need to make the decision.

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.

The head of Lebanon's Hezbollah group, Naim Qassem, will give a speech on Tuesday, Hezbollah's media office said, minutes after Hochstein made his remarks about a "real opportunity" to end the conflict.

There are signs of progress on at least one front of the conflict in the Middle East. CBS News senior foreign correspondent Elizabeth Palmer has the latest on reports of a cease-fire deal between Israel and Iran-backed Hezbollah in Lebanon.

Iran’s supreme leader is said to be pushing Hezbollah towards a ceasefire with Israel as US mediators head to Lebanon to try to broker a deal.

US special envoy Amos Hochstein arrived in the Lebanese capital on Tuesday for talks with officials on a truce plan, which Lebanon has largely endorsed, to halt the Israel-Hezbollah war. Another government official said Lebanon was "waiting for US special envoy Amos Hochstein to arrive so we can review certain outstanding points with him".

A rare Israeli strike in central Beirut killed the Hezbollah militant group's chief spokesman on Sunday, while an Israeli strike in northern Gaza's Beit Lahiya killed at least 30 people, a hospital director there told The Associated Press.