Gas production would be based on the Lebanese side, but Israel would be compensated for gas extracted from its side of the line, under a separately signed deal between Total and Israel, the company says.
Lebanon hopes that demarcating maritime borders will pave the way for gas exploration to help lift it out of its crippling economic crisis.
Lebanese authorities are discussing the alleged violation with a United Nations Interim Force on the heels of the maritime border deal between the two countries.
Lebanese lead negotiator Elias Bou Saab said it would be a "historic deal" if everything goes well.
Israel has given London-listed drilling company Energean the green light to start testing gas pumping in the Karish gas field disputed with Lebanon, despite threats made by Hezbollah.
A meeting between Lebanese President Michel Aoun and US Ambassador Dorothy Shea has resulted in a proposed solution to the maritime border dispute with Israel.
President Uhuru Kenyatta slams ruling by UN's top court that largely went in favour of Somalia and gave Kenya only a small slice of the disputed tract of the sea off the East African coast.
Lebanon and Israel have begun unprecedented talks sponsored by the UN and US to settle a maritime border dispute and clear the way for oil and gas exploration.
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