NAQOURA, Lebanon (Reuters) -France's foreign minister said on Sunday there had been progress in discussions with senior officials in Lebanon aimed at easing tensions between Hezbollah and Israel and preventing a war breaking out.

France has historical ties with Lebanon and earlier this year Foreign Minister Stephane Sejourne proposed Hezbollah's elite unit pull back 10 km (6 miles) from the Israeli border, while Israel would halt strikes in southern Lebanon.

The written proposal also looked at long-term border issues and had been discussed with partners including the United States, which has its own efforts to ease tensions and exerts the most influence on Israel.

Israel and Hezbollah have traded tit for tat strikes in recent months, but the exchanges have increased since Iran launched missiles on Israel in response to a presumed Israeli airstrike on April 1 that destroyed part of Iran's embassy compound in Damascus killing several Iranian officers.

More Israeli strikes hit southern Lebanon overnight close to the United Nations' peacekeeping force UNIFIL, according to military officials, just hours before Sejourne visited its headquarters in Naqoura in southern Lebanon.

"If I look at the situation today if there were not a war in Gaza, we could be talking about a war in southern Lebanon given the number of strikes and the impact on the area," Sejourne said after speaking to UNIFIL commanders.

Speaking after meeting the influential speaker of parliament Nabih Berri, an ally of Hezbollah, and the head of the Lebanese army Joseph Aoun, Sejourne said there had been "a lot of progress" over the French proposals. He did not elaborate.

The UNIFIL mission, as well as unarmed technical observers known as UNTSO, are stationed in southern Lebanon to monitor hostilities along the demarcation line between Lebanon and Israel, known as the Blue Line. France has 700 troops who are part of the 10,000-strong UNIFIL.

Hezbollah has said it will not enter any concrete discussion until there is a ceasefire in Gaza, where the war between Israel and Islamist militant group Hamas is in its seventh month.

Israel has flagged a potential military operation along its northern front, saying it wants to restore calm on the border with Lebanon so that thousands of displaced Israelis can return to the area without fear of rocket attacks.

In a letter addressed to the French embassy in Beirut in March, Lebanon's foreign ministry said Beirut believed the French initiative would be a significant step towards peace and security in Lebanon and the broader region.

Lebanese media had reported the government had provided feedback to the French on the proposal but French officials say the responses so far have been general and lack consensus among the Lebanese.

Sejourne will discuss Lebanon with Arab and Western states in Riyadh, Saudi Arabia, on Monday before relaying the latest Lebanese positions in Israel later in the week.

(Reporting by John Irish;Editing by Mathieu Rosemain, Elaine Hardcastle and Ros Russell)

By John Irish