Israel was all but certain to miss Sunday's deadline, which is part of a ceasefire agreement that ended its war with the Iran-backed Hezbollah group two months ago.

The deal that took effect on November 27 said the Lebanese army was to deploy alongside United Nations peacekeepers in the south as the Israeli army withdrew over a 60-day period.

That period ends on Sunday.

Lebanon's health ministry said Israeli forces opened fire on "citizens who were trying to return to their villages", killing 11 and wounding 83.

The ministry's toll includes a soldier from the Lebanese army, which also announced his death and said Israeli fire had wounded another soldier.

AFP journalists said convoys of vehicles carrying hundreds of people, some flying yellow Hezbollah flags, were trying to get to several villages despite the Israeli military's continued presence.

"We will return to our villages and the Israeli enemy will leave," even if it costs lives, said Ali Harb, a 27-year-old trying to go to Kfar Kila.

- Pictures of Nasrallah -

Residents could also be seen heading on foot and by motorbike towards the devastated border town of Mays al-Jabal, where Israeli troops are still stationed.

Some held up portraits of slain Hezbollah leader Hassan Nasrallah, while women dressed in black carried photos of family members killed in the war.

Israeli military spokesman Avichay Adraee had issued a message earlier on Sunday to residents of more than 60 villages in southern Lebanon telling them not to return.

Speaking from the border town of Aita al-Shaab, Hezbollah lawmaker Hassan Fadlallah hailed in a television appearance "the return of residents in spite of the threats and warnings".

Lebanese President Joseph Aoun, the former army chief who took office earlier this month after a two-year vacancy in the post, called on residents to keep a cool head and "trust the Lebanese army", which he said wanted "to ensure your safe return to your homes and villages".

On Saturday, the army had said the delay in implementing the agreement was the "result of the procrastination in the withdrawal from the Israeli enemy's side".

A joint statement from the UN special coordinator for Lebanon and the head of the UN peacekeeping mission on Sunday acknowledged "that the timelines envisaged in the November Understanding have not been met".

"As seen tragically this morning, conditions are not yet in place for the safe return of citizens to their villages along the Blue Line," the statement said, referring to the border. It urged residents "to exercise caution".

Israeli forces have left coastal areas of southern Lebanon, but are still present in areas further east.

The ceasefire deal stipulates that Hezbollah pull back its forces north of the Litani River -- about 30 kilometres (20 miles) from the border -- and dismantle any remaining military infrastructure in the south.

But Israeli Prime Minister Benjamin Netanyahu's office said on Friday that the "agreement has not yet been fully enforced by the Lebanese state", so the military's withdrawal would continue beyond the Sunday deadline.

The Lebanese army said it was "ready to continue its deployment" as soon as Israel left.

Lebanese caretaker Prime Minister Najib Mikati called Sunday for the backers of the ceasefire agreement -- a group that includes the United States and France -- "to force the Israeli enemy to withdraw".

- Demolitions -

Lebanese state media have reported that Israeli forces have carried out demolitions in villages they control.

Aoun spoke on Saturday with his French counterpart Emmanuel Macron about the "need to oblige Israel to respect the terms of the deal", adding it must "end its successive violations, including the destruction of border villages".

Macron's office said the French president had called on all parties to the ceasefire to honour their commitments as soon as possible.

The fragile truce has generally held, even as the warring sides have repeatedly traded accusations of violations.

The deal ended two months of full-scale war that had followed nearly a year of low-intensity exchanges.

Hezbollah began trading cross-border fire with the Israeli army the day after the October 7, 2023 attack on Israel by its Palestinian ally Hamas, which triggered the war in Gaza.

Israel's campaign delivered a series of devastating blows against Hezbollah's leadership including its longtime chief Nasrallah.