U.S. mediators are working on a proposal to halt hostilities between Israel and Lebanese armed group Hezbollah, starting with a 60-day cease-fire, two sources said on Wednesday, but Israel pressed its offensive, bombarding Lebanon’s historic city of Baalbek after issuing a mass evacuation order.

The sources — a person briefed on the talks and a senior diplomat working on Lebanon — told Reuters the two-month period would be used to finalize full implementation of United Nations Security Council Resolution 1701, adopted in 2006 to keep southern Lebanon free of arms outside state control.

A U.S. official said White House officials Brett McGurk and Amos Hochstein will visit Israel on Thursday to engage on a range of issues “including Gaza, Lebanon, hostages, Iran and broader regional matters.”

Hezbollah’s new leader Naim Qassem said the Iran-backed group would agree to a cease-fire within certain parameters if Israel wanted to stop the war, but said Israel had so far not agreed to any proposal that could be discussed.

It was Qassem’s first speech as secretary-general, a day after Hezbollah announced his election to the post after Israel assassinated the group’s longtime leader Hassan Nasrallah.

The latest cease-fire efforts come as Israel’s operation against Hezbollah in Lebanon continues to expand.

Its army launched heavy airstrikes on Wednesday on the eastern city of Baalbek, famed for its Roman temples, and nearby villages, security sources told Reuters, following an Israeli evacuation order.

Tens of thousands of mostly Shi’ite Muslim Lebanese, including many who had sought shelter in the city from other areas, fled after the warning was issued.

Bilal Raad, the regional head of the Lebanese civil defense, said the largely volunteer force had been calling on residents to leave via megaphones after receiving phone calls from someone identifying themselves as being from the Israeli military.

“People are all over each other, the whole city is in a panic trying to figure out where to go, there’s a huge traffic jam,” he said ahead of the bombardment.

Some of the areas they are fleeing to are already full of displaced people.

Antoine Habchi, a lawmaker representing Christian-majority Deir al-Ahmar to the northwest of Baalbek, said more than 10,000 people were already sheltering in homes, schools and churches.

“We welcome everyone, of course, but we need immediate government help so that these people don’t stay out in the cold,” he told Reuters.

For a third straight day, Hezbollah reported intense fighting with Israeli forces in or around the southern town of Khiyam — the deepest Israel’s troops have been reported to have penetrated into Lebanon since fighting began.

‘Earnest push’

Resolution 1701 has been the cornerstone of talks to end the last year of fighting between Israel and Hezbollah, which erupted in parallel with the war in Gaza and has dramatically escalated over the last five weeks.

“We’d like to reiterate that we seek a diplomatic resolution that fully implements 1701 and gets both Israeli and Lebanese citizens back to their homes on both sides of the border,” said Sama Habib, spokesperson at the U.S. embassy in Beirut, when asked about the reported proposal.

U.S. envoy Hochstein told reporters in Beirut earlier this month that better mechanisms for enforcement were needed as neither Israel nor Lebanon had fully implemented the resolution.

The two sources told Reuters that the 60-day truce has replaced a proposal last month by the United States and other countries that envisioned a cease-fire for 21 days as a prelude to 1701 coming into full force.

Both, however, cautioned that the deal could still fall through. “There is an earnest push to get to a cease-fire, but it is still hard to get it to materialize,” the diplomat said.

Israel’s Channel 12 television reported that Israel was seeking a reinforced version of U.N. Resolution 1701, to allow Israel to intervene if it felt its security threatened.

Lebanon had not yet been formally briefed on the proposal and could not comment on its details, Lebanese officials said.

The push for a cease-fire for Lebanon comes days before the U.S. presidential election and in parallel with a similar diplomatic drive on Gaza.