U.S. mediators are working on a proposal to wind down hostilities between Israel's military and Iran-backed Lebanese armed group Hezbollah, beginning with a 60-day cease-fire, two sources with knowledge of the talks told Reuters on Wednesday.

The sources – a person briefed on the talks and a senior diplomat working on Lebanon – said 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.

"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 proposal.

The latest effort comes as Israel's operation in Lebanon continues to expand. Its army on Wednesday issued a first evacuation order for the eastern city of Baalbek, where tens of thousands of Lebanese, including many who had fled other areas, were residing.

Such notices are usually followed by bombardment. Residents started to flee the city, leading to heavy traffic, but others stayed put as there was nowhere safe to go, former mayor Fuad Ballouk told Reuters.

For a third straight day, Hezbollah reported intense fighting with Israeli forces near the southern town of Khiyam – the deepest Israel's troops have been reported to have penetrated into Lebanon since fighting began.

Israeli strikes on south Lebanon's Sarafand killed at least 10 people Tuesday – most of them women and children – while a separate strike on the port city of Sidon killed at least five people and injured 37, Lebanese authorities said.

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.

U.S. presidential envoy Amos Hochstein, who is working on the new cease-fire proposal, 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 senior diplomat and the source briefed on the talks 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.

The person briefed on the talks said one element Israel was still pushing for was the ability to carry out "direct enforcement" of the truce via air strikes or other military operations against Hezbollah if it was violating the deal.

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.

Axios reported that Hochstein and U.S. presidential adviser Brett McGurk will land in Israel on Thursday to try to close the deal on Lebanon, which could be implemented within weeks, according to three unnamed sources.

Hochstein and McGurk are expected to meet with Israeli Prime Minister Netanyahu, Defence Minister Yoav Gallant and Minister for Strategic Affairs Ron Dermer, according to the Axios report.

Israeli and U.S. officials believe that Hezbollah is finally willing to disconnect itself from Hamas in Gaza after some of the blows that the Lebanese group has faced over the past two months, including the killing of its leader Hassan Nasrallah, the Axios report said.

The U.S. State Department did not immediately respond to a request for comment.