Israel's Security Cabinet met on Sunday to consider Gaza proposals.
A Palestinian teenager died Monday of wounds he suffered during anti-Israel protests along the Gaza-Israel border, the Gaza Health Ministry said.
A member of the Israeli Security Cabinet, Ze'ev Elkin (Likud), referred to the ceasefire talks with Palestinian resistance movement Hamas and said that "an arrangement with the organization is now not on the agenda".
Asked about Cairo's role in the truce talks, Zeev Elkin, a member of Israeli Prime Minister Benjamin Netanyahu's security cabinet and Likud party, said Egyptian security needs meant the Arab power "understands that it can not shrug off Gaza".
Husam Badran, a member of the "Hamas" politburo, offered Sunday assurances that the movement would not agree to establish a state in Gaza and would not reach any political arrangement without Palestinian national consensus.
Israel's Defence Ministry described the barrier as "an impenetrable breakwater".
According to al-Hayat al-Jadida, thousands protested in the city of Tel Aviv and other Arab towns in Israel against Israel's racist recent nation-state law. A spokesman said any deal risked ending hopes of achieving Palestinian statehood.
Israel is building a big fence on the sea border with the Gaza strip. Fatah claims that such transaction, a "free gift" for Israel, and proposed a truce - part of the efforts of the President of the United States to eliminate the Palestinian cause within the framework of his plan for peace in the middle East.
Also on Sunday, the Israeli military said it fired toward a vehicle used by Palestinian balloon-launchers in Gaza on Sunday.
Israel and Hamas came close to serious conflict recently when months of border violence escalated.
As soon as news of the reported proposal broke Friday, the families of Israeli fallen soldiers and civilians held in Gaza appealed to Prime Minister Benjamin Netanyahu and other Israeli political leaders, urging them to include the release of Israelis in any deal.
There are more than 4000 fishers and around 700 boats in the Gaza Strip providing livelihood to at least 70.000 Palestinians, while the Israeli military and navy keep attacking them, kidnapping them and confiscating their boats, in addition to the dozens of casualties, including fatalities, resulting from these violations.