The Lebanese and Syrian presidents agreed on the need to "control the border" between the two countries, after the two countries had traded accusations over cross-border gunfire.

Lebanese President Joseph Aoun received a phone call from his Syrian counterpart, Ahmad al-Sharaa, during which they agreed that "the current sensitive situation requires enhancing coordination and consultation... especially with regard to the necessity of controlling the border", a Lebanese presidency statement said.

A U.S. diplomatic initiative has been launched to address the Lebanese situation but this move does not mean Washington is concerned with an immediate halt to the Israel-Hezbollah war, well-informed sources said.

The last residents of a Christian village on Lebanon's border with Israel fled the area on Tuesday, a U.N. source and an AFP correspondent said, after locals had for days defied an Israeli order to leave.

Fighting flared last week between Israel and Hezbollah as part of a wider regional war, prompting the Israeli military to warn people across swathes of southern Lebanon to flee.

Residents of the southern border town of Alma al-Shaab, a predominantly Christian village, were evacuating their village Tuesday after Israeli warnings.

The mayor of another Chrisitan village, also in south Lebanon, said he received a direct call from the Israeli army, warning him that displaced people from neighboring Shia-majority villages would put his village, Rmeish, in danger and turn it into a military target.

Former minister Mohammad Fneish has in recent days visited Speaker Nabih Berri in Ain el-Tineh, carrying a verbal message from Hezbollah Secretary-General Sheikh Naim Qassem.

According to An-Nahar newspaper, the message focused on the following points:

The Israeli army has issued a warning to the residents of Ghbayri, Hadath, Haret Hreik, Laylaki, Burj al-Barajne, Shiyyah and Tahwitat al Ghadir.

Earlier in the day, Israel had warned residents of Tyre's Abbasiyyeh and the coastal town of Sidon to evacuate areas near two threatened buildings.

The Israeli army is preparing for a prolonged offensive against Hezbollah, aiming to weaken the group to prevent the constant evacuation of northern residents, according to sources cited by the Financial Times.

The United Nations said Tuesday that more than 100,000 people had been newly displaced within Lebanon in just 24 hours amid the war raging in the Middle East.

"As of today, more than 667,000 people in Lebanon have now registered on the (Lebanese) government's online platform as displaced -- and this is an increase of 100,000 in just one day," said Karolina Lindholm Billing, the U.N. refugee agency's representative in Lebanon.

President Joseph Aoun voiced Tuesday his full support for the Lebanese Army as he met with Army Commander Rodolphe Haydal and Defense Minister Michel Menassah in Yarzeh.

Aoun said he will stand "as a bulwark" against any attacks on the military institution or its leadership.

Israel's military said Tuesday it would soon strike Hezbollah infrastructure in the southern Lebanese cities of Tyre and Sidon, warning residents to move away from targeted buildings.

"Urgent warning to the residents of Tyre and Sidon. The IDF will soon attack military infrastructure belonging to the terrorist organisation Hezbollah," one of the military's Arabic-language spokesmen, Avichay Adraee, posted on X.