Correction: A previous version of this article incorrectly said Menachem Klein is a political scientist at Hebrew University. He is a political scientist at Bar Ilan University. This version has been corrected.

Israeli soldiers are seen in a staging area near the border with the northern Gaza Strip on August 18, 2014. (Amir Cohen/Reuters)

Israeli and Palestinian officials agreed just before a midnight deadline Monday to extend the Gaza cease-fire for an additional 24 hours to try to complete a deal that could lead to a permanent truce.

The two sides will continue talking in Cairo. A senior Israeli official said they had agreed to extend the deadline at Egypt’s request. Earlier, the Palestinian delegation sent mixed signals on whether a deal was close.

The Palestinian death toll reached 2,016 Monday, according to the Gaza Health Ministry, which is run by the militant group Hamas, after dozens of Palestinians succumbed to injuries and more bodies were found in rubble. The dead included 541 children under 18, the ministry said.

Sixty-four Israeli soldiers have been killed in the conflict, along with two Israeli civilians and one guest worker.

At the Cairo talks, Israel is seeking guarantees of “peace and quiet,” a cessation of all rocket fire and tunnel operations, and, ultimately, the disarming of the Gaza Strip.

Hamas fighters in Gaza said they are ready to resume attacks on Israel from tunnels, which they said have survived Israeli bombardment. (Reuters)

For their part, Hamas, which controls the coastal enclave, and the Palestinian Authority, which controls the West Bank, want an opening of all border crossings and an end to the trade and travel restrictions imposed by Israel and Egypt that make Gaza, in the Palestinians’ words, “an open-air prison.” The Palestinians want restrictions on building materials lifted, and they are requesting permission to build a seaport and rehabilitate Yasser Arafat International Airport, which has been closed for 13 years.

Israel is seeking support for its view that any arrangement with Hamas, whether a signed cease-fire or something short of that, must allow Israel to return to Gaza to destroy new or rebuilt tunnels.

“The way we dealt with the tunnel issues was a mistake,” said Israeli Deputy Foreign Minister Tzahi Hanegbi. “We knew about them, we had enough intelligence about this strategic threat” but miscalculated by thinking that the threat was containable.

“This policy is not going to repeat itself,” he said.

Hanegbi was in Washington for meetings at the State Department as Israel tries to repair strains in its relationship with the Obama administration over the Gaza operation. Israel has no intention of reoccupying Gaza, despite domestic political pressure to do so, Hanegbi said.

As talks went to the wire in Cairo, Israel’s domestic security agency said Monday it had penetrated Hamas cells in the West Bank that it said were planning a coup to topple Palestinian Authority President Mahmoud Abbas.

The statement by the Shin Bet agency included names of alleged ringleaders, organizational flow charts and photographs of weapons seized. The cache included 24 rifles, six pistols and seven rocket launchers — not much for a coup.The Palestinian Authority maintains a vigorous security force in the West Bank, alongside the Israeli troops and police there.

Shin Bet said that it began arresting members of the alleged conspiracy in May and that it confiscated $170,000 that was to be used to organize cells and recruit members. The mastermind of the plot, the agency said, was senior Hamas leader Salah al-Arouri, who now lives in Turkey after serving a prison sentence in Israel.

Previously, Israeli authorities accused Arouri of sponsoring a Hamas cell that kidnapped and killed three Israeli teenagers in June.

Also Monday, Israeli troops and police resumed the controversial practice of demolishing the family homes of terrorism suspects, in this case the two men who Israeli authorities say killed the teenagers. The demolitions took place near Hebron, and crowds of young people hurled stones in protest.

Israeli news media said pointedly that Shin Bet’s announcement seemed timed to undermine Palestinians who were trying to project a unified face at the cease-fire talks.

“I don’t buy it,” said Menachem Klein, a political scientist at Bar Ilan University.

“The announcement speaks about infrastructure for future terrorist or guerrilla operations,” he said. “But the evidence of arms and ammunition was not enough to take over a neighborhood, not to mention the West Bank.”

Gearan reported from Washington. Orly Halpern contributed to this report.