Lebanon has secured its "full rights" in the latest text drafted by U.S. mediators to demarcate the maritime border with Israel, its lead negotiator said Tuesday, after Israel said it met its terms too.

"Lebanon has obtained its full rights, and all of its remarks have been taken into account," said lead negotiator Elias Bou Saab, the deputy speaker of parliament, after handing the draft to President Michel Aoun.

Both Lebanon and Israel have said that they are satisfied with a draft submitted overnight by U.S. mediator Amos Hochstein and that the draft may lead to a "historic" sea border demarcation deal that will allow both sides to explore for huge reserves of gas off their Mediterranean coasts.

Hochstein submitted an initial set of proposed final terms to Israel and Lebanon earlier this month.

President Michel Aoun on Monday said he hopes for a gas deal with Israel to be reached within the "next few days."

Lebanon is inclined to agree in principle to the U.S. proposal regarding sea border demarcation with Israel, a Lebanese diplomatic source said.

The country will “link the final approval to the return of the Naqoura meetings, in which the documents will be formulated and the technical coordinates will be specified,” the source told Russia’s Sputnik news agency.

President Michel Aoun has received a phone call from U.S. mediator Amos Hochstein, who briefed him on the outcome of the latest round of talks with the Lebanese and Israeli sides, the Presidency said.

“Mr. Hochstein clarified that the discussion rounds have been concluded… and over the next few hours he will send a version that includes the final format of the proposal related to the demarcation of the southern maritime border,” the Presidency added.

London-listed firm Energean has begun testing pipes between Israel and the Karish offshore gas field, a key step towards production from the eastern Mediterranean site, a source of friction between Israel and Lebanon.

Israeli Defense Minister Benny Gantz has said that Israel would move ahead with plans to extract gas from the Karish field even if no deal is reached Lebanon, warning Hezbollah that any attack would meet a “resolute” response, the Times of Israel has reported.

“If Hezbollah makes that mistake and attacks Israel in any way, by air, sea or land, Israel will defend itself resolutely, it will attack resolutely, and if things develop into a broader conflict, we will take Lebanon apart, and that would be a great pity,” he told Channel 12, according to the Israeli newspaper.

Maronite Patriarch Beshara al-Rahi on Sunday rejected what he called the election of a “settlements president.”

Turning to the issue of the new government, al-Rahi called for the formation of “an inclusive rather than a partisan government.”

The French intervened following the latest Israeli rejection in the gas talks with Lebanon and Paris told Beirut through PM-designate Najib Mikati that "Israel does not intend to escalate," al-Akhbar newspaper quoted prominent sources as saying.

While the Israeli "political shelling" against the draft gas agreement with Lebanon has "calmed down," Deputy Speaker Elias Bou Saab has received from U.S. mediator Amos Hochstein a letter containing Israel's remarks to the draft and Israel's comments on the proposed Lebanese amendments, al-Akhbar daily said on Saturday.