Israel chose to erect a sea barrier in 2014, when several Hamas gunmen tried to enter Israel by sea but were shot dead by soldiers.
Palestinian sources told Ynet that the Hamas meeting took place in response to the Israeli statement and that Hamas leaders warned they could inflict casualties that the Israeli public and government would not be able to tolerate.
Israeli Prime Minister Benjamin Netanyahu earlier convened his cabinet to possibly approve proposals made by the United Nations (UN) and Egypt for preventing another war on Gaza.
Senior PLO official Ahmed Majdalani said any agreement with Israel should not be limited to "Hamas".
In return, the PA would resume paying its employees in Gaza whose salaries it has withheld, the TV report said. "With every day that passes, our counter terrorism capabilities around the Gaza Strip are growing stronger".
Member of the political bureau of Hamas Husam Badran, center, speaks at the Israel-Gaza border, east of Gaza city on August 3, 2018.
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The movement does not have the authority to strike any deal with Israel, he said.
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".
It is the latest phase of border demonstrations that began at the end of March, in which at least 159 Palestinians have been killed while one Israeli soldier has been shot dead.
The protests have also seen Palestinians fly airborne incendiary devices toward Israeli territory, sparking hundreds of fires in southern Israel and causing millions of shekels in estimated damages.
The Asharq al-Aswat story indicates that Hamas wants a "gradual" cease-fire, the first stage of which Hamas would stop its terror activities against Israel from the Gaza Strip, including rocket firings and arson attacks with incendiary kites and balloons, as well as attempts by Gaza protesters to cross into Israel.
The Israel Defense Forces confirmed in a statement that an aircraft fired at the group in the northern Gaza Strip.