The UN and Egypt are now trying to secure a deal between Israel and Hamas for a lasting truce.
Galant said what is at issue is a cease-fire, not a full-scale agreement.
Highlighting skepticism over a long-term ceasefire, Hamas's political leadership met on Monday with top officials in its military to discuss its preparedness for battle with Israel, according to a report in Israeli news site Ynet.
Minister of Jerusalem and Environmental Protection Zeev Elkin (L) and Cabinet Secretary Tzachi Braverman (R) attend a special cabinet meeting marking Jerusalem Day, at the Bible Lands Museum in Jerusalem May 13, 2018.
The difference of perceptions suggests chances for agreement are slim.
Israel and Hamas came close to serious conflict recently when months of border violence escalated.
Israel also imposed a blockade of Gaza that year, and the United Nations has since warned that the Strip would be "unlivable" by 2020 if the blockade is not lifted. Twenty-four of slain protesters were minors, the ministry has said.
Israel has rejected accusations of unlawful use of lethal force, alleging that Hamas has used the protests as cover to carry out attacks and infiltrate into its territory.
The protests have been marked by clashes as some protesters hurl stones at Israeli soldiers and attempt to breach the border fence, at times laying explosive devices on the fence and using incendiary kites to set ablaze Israeli fields, torching extensive patches of agricultural land near the border. Fires started by the home-made devices have burned large areas near Gaza, including fields.
"As far as we are concerned, after the State of Israel left Gaza, responsibility should not be imposed on us".
The deputy head of Hamas's politburo, Saleh al-Arouri, who served several Israeli jail terms for terrorism, arrived in the Gaza Strip late Thursday with other Hamas leaders for talks focused on renewed reconciliation efforts with Fatah and to raise the truce prospects with the terror group's Gazan leadership, Hamas-linked media reported.
Still, in what Palestinians saw a goodwill gesture, Egyptian cooking oil began entering Gaza on Sunday, offsetting Israeli supplies cut off in retaliation for the border violence.
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