BEIRUT/PARIS - France has delivered a written proposal to Beirut aimed at ending hostilities with Israel and settling the disputed Lebanon-Israel frontier, according to a document seen by Reuters that calls for fighters including Hezbollah's elite unit to withdraw 10 km (6 miles) from the border.

The plan aims to end fighting between the Iran-backed Hezbollah and Israel at the border. The hostilities have run in parallel to the Gaza war and are fueling concern of a ruinous, all-out confrontation.

The document, the first written proposal brought to Beirut during weeks of Western mediation, was delivered to top Lebanese state officials including Prime Minister Najib Mikati by French Foreign Minister Stephane Sejourne last week, four senior Lebanese and three French officials said.

It declares the aim of preventing a conflict "that risks spiraling out of control" and enforcing "a potential ceasefire, when the conditions are right" and ultimately envisions negotiations on delineation of the contentious land border between Lebanon and Israel.

Hezbollah rejects formally negotiating a de-escalation until the war in Gaza ends, a position reiterated by a Hezbollah politician in response to questions for this story.

While some details of similar mediation efforts by U.S. Middle East envoy Amos Hochstein have been circulating in recent weeks, the full details of the French written proposal delivered to Lebanon have not previously been reported.

The three-step plan envisages a 10-day process of de-escalation ending with the border negotiations.

One French diplomatic source said the proposal had been put to the governments of Israel, Lebanon and Hezbollah.

France has historical ties with Lebanon. It has 20,000 citizens in the country and some 800 troops as part of a U.N. peacekeeping force.

"We made proposals. We are in contact with the Americans and it's important that we bring together all initiatives and build peace," Sejourne told a news conference on Monday.

The plan proposes Lebanese armed groups and Israel would cease military operations against each other, including Israeli airstrikes in Lebanon.

Several non-state groups, including Palestinian factions, have mounted attacks on Israel from south Lebanon during the latest hostilities, though Hezbollah is the dominant power in the area with a fighting force widely seen to outgun the Lebanese army.