Fresh Israeli strikes hit Beirut's southern suburbs and south Lebanon on Tuesday after the Israeli army warned people to evacuate, with Lebanese authorities saying nearly 760,000 people had been registered as displaced.

The U.S. administration has delivered an urgent message to President Joseph Aoun, calling for a move toward negotiations with Israel, An-Nahar newspaper said on Tuesday.

Prime Minister Nawaf Salam had previously received the same message during meetings with American and other Western officials, the daily said.

A German court on Tuesday jailed a 35-year-old man for supplying Hezbollah with equipment for drones.

Speaker Nabih Berri on Tuesday held talks with ex-PMs Najib Mikati, Fouad Saniora and Tammam Salam, discussing with them the political and military developments in Lebanon in light of Israel's continued attacks.

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.