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France's top diplomat on Sunday urged calm in Lebanon during his second visit to the country since cross-border tensions with Israel flared on the back of the war in Gaza.

Israel and Lebanon's Iran-backed Hezbollah group have exchanged near-daily fire since the start of Israel's war on Gaza on October 7. Hezbollah says its attacks aim to divert some Israeli attention away from Gaza.

Fighting has intensified in recent weeks, with Israel striking deeper into Lebanese territory, while Hezbollah has stepped up its missile and drone attacks on military positions in northern Israel.

The United States has led diplomatic efforts to halt violence along the border with Israel, with France also seeking ways to de-escalate tensions.

Paris presented to both Lebanon and Israel an initiative in January seeking to end hostilities.

During a visit to the headquarters of the United Nations' peacekeeping mission in southern Lebanon (UNIFIL), French Foreign Minister Stephane Sejourne reiterated that Paris has been making proposals to "avoid war in Lebanon".

"I will head to Beirut to meet political authorities to... make proposals," he added. "Our responsibility is to mitigate escalation, and that is also our role in UNIFIL. We have 700 soldiers here."

Hezbollah has repeatedly declared that only a ceasefire in Gaza will put an end to its attacks on Israel.

A French diplomatic source told AFP that the volume of cross-border attacks had doubled since April 13.

Sejourne is set to meet Lebanese officials on Sunday afternoon ahead of holding a press conference.

He met with influential Parliament Speaker Nabih Berri, a Hezbollah ally.

"Lebanon is waiting for the French proposal that seeks de-escalation and an end to hostilities," Berri said after the meeting in a statement carried by Lebanon's official National News Agency.

In March, Beirut submitted its response to the French initiative, which was based on UN Security Council Resolution 1701, which ended the Hezbollah-Israel 2006 war.

Lebanon moves towards accepting ICC jurisdiction for war crimes on its soil.

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The resolution called for the removal of weapons in southern Lebanon from the hands of everyone except the army and other state security forces.

Lebanese officials have also referred to the resolution, which states that Israeli troops should withdraw from Lebanon, to demand Israel pull out from disputed border territory.

Berri insisted on implementing the UN resolution, according to his statement.

Lebanese Prime Minister Najib Mikati, who heads a caretaker government with reduced powers, on Friday suggested that Paris was reviewing its proposal and would submit a new one to Beirut.

Sejourne's trip - which will also see him stop in Riyadh for a summit on Gaza - coincides with a visit to Jerusalem by US envoy Amos Hochstein as Washington also pushes for de-escalation along the Israel-Lebanon border.

Since October 8 at least 385 people have been killed in Lebanon, including 254 Hezbollah fighters and dozens of civilians, according to an AFP tally.

Israel says 11 soldiers and nine civilians have been killed on its side of the border, but Hezbollah believes the number to be higher.

Tens of thousands of people have been displaced on both sides.