Lebanon and Hezbollah have agreed to a U.S. proposal for a cease-fire 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 the fighting.

Ali Hassan Khalil, an aide to Parliament Speaker Nabih Berri, said Lebanon had delivered its written response to the U.S. ambassador in Lebanon on Monday, and White House envoy Amos Hochstein was traveling to Beirut to continue talks.

There was no immediate comment from Israel.

Hezbollah, a heavily armed movement backed by Iran, endorsed its longtime ally Berri to negotiate over a cease-fire.

"Lebanon presented its comments on the paper in a positive atmosphere," Khalil said, declining to give further details. "All the comments that we presented affirm the precise adherence to [U.N.] Resolution 1701 with all its provisions."

He was referring to U.N. Security Council Resolution 1701, which ended a previous war between Hezbollah and Israel in 2006.

Its terms require Hezbollah to have no armed presence in the area between the Lebanese-Israeli border and the Litani River, which runs some 20 miles north of the frontier.

Khalil said the success of the initiative now depended on Israel, saying if Israel did not want a solution, "it could make 100 problems."

Israel has long claimed that Resolution 1701 was never properly implemented, pointing to the presence of Hezbollah fighters and weapons along the border. Lebanon has accused Israel of violations including flying warplanes in its airspace.

Khalil said Israel was trying to negotiate "under fire," a reference to an escalation of its bombardment of Beirut and the Hezbollah-controlled southern suburbs.

"This won't affect our position," he said.