Israeli Foreign Minister Israel Katz said Monday "time is running out" to reach a diplomatic solution in south Lebanon, as tensions flare between the two countries, with daily cross-border fire.

"Israel will act militarily to return the evacuated citizens" to its northern border area if no diplomatic solution is reached to end the violence, Katz told his visiting French counterpart Stephane Sejourne, according to a statement issued by the Israeli foreign ministry.

Parliament Speaker Nabih Berri has heard from the Quintet's ambassadors that there is no veto on any presidential candidate.

Berri told al-Jadeed TV on Sunday that all the ambassadors including the Saudi ambassador have told him that the Quintet has no candidates and no veto on any name but would rather help the Lebanese choose their own president.

U.S. President Joe Biden's Middle East envoy Amos Hochstein has outlined the key elements of a proposed political settlement to deescalate tensions between Israel and Hezbollah during his visit to Israel on Sunday, Israeli newspaper Yedioth Ahronoth reported.

Hezbollah announced Monday the death of three of its members, as Israeli artillery shelled the outskirts of Dhaira, Tayr Harfa, al-Jebbayn and Zibqine in south Lebanon.

Hezbollah later claimed two attacks on Israeli posts in the occupied Shebaa Farms and Israel bombed the border towns of Mays al-Jabal, Rashaya al-Fokhar, Baraachit, al-Labbouneh, al-Naqoura, and Shihine.

Israel has attacked more than 50 Hezbollah targets in Syria and 3,400 in Lebanon since the war with Hamas in Gaza began in October, Israeli army spokesman Daniel Hagari said.

When Inas Tehini and her family fled their south Lebanon village after Hezbollah and Israel began exchanging fire in October, she thought they would be home in a matter of days.

But nearly four months later in a school turned shelter, her hopes for a swift return to normality have faded after Israeli strikes badly damaged the family home in Aita al-Shaab on the border, said the mother of three.

Israel's military has issued its most detailed warning yet to Hezbollah that it would be "ready to attack immediately" if provoked, as it recounted its actions along the Lebanese border during four months of war in Gaza and made a rare acknowledgement of dozens of airstrikes inside Syria against the Lebanese group.

"We do not choose war as our first priority, but we are certainly prepared," military spokesperson Daniel Hagari said, adding: "We will continue to act wherever Hezbollah is present, we will continue to act wherever it is required in the Middle East. What is true for Lebanon is true for Syria, and is true for other more distant places."

Israeli Defense Minister Yoav Gallant has warned that a potential pause in the Israel-Hamas war in Gaza will not apply to the ongoing hostilities with Lebanon’s Hezbollah.

“If Hezbollah thinks that when there’s a pause in fighting in the south (Gaza), we will hold fire against it, it’s sorely mistaken,” Gallant said after meeting troops from the Israeli army’s Alpine Unit on Mount Hermon, according to a statement from his office.

The Amal Movement confirmed Saturday that two of its fighters were killed in an Israeli airstrike overnight in the southern border town of Blida.

UK Foreign Secretary David Cameron has ended a one-day visit to Lebanon. This is his first official visit to the country as Foreign Secretary, following his previous visit as Prime Minister in September 2015 and his fourth visit to the Middle East as Foreign Secretary.