This video, released by the Israel Defense Forces (IDF), shows two methods for warning Palestinian civilians of an upcoming airstrike. The first part of the video features an audio recording of a call made by an IDF representative to a Palestinian citizen, warning them that they should leave the building they are in as it is about to be targeted. The second part shows the Israeli military shooting a small “warning missile” at a building in Palestine designed to warn occupants that the building will soon be destroyed. (Israel Defense Forces)

Israel on Tuesday accepted an Egyptian proposal for a cease-fire with Hamas in Gaza after a week of non-stop fire, but the Islamist militant group appeared to reject the deal, saying it had not been consulted on its terms.

A senior Hamas official, Sami Abu Zuhri, called the proposal “unacceptable” and complained that Egyptians have not spoken with the Gaza leadership. The group’s armed wing, the Qassam Brigade, wrote on its Web site that the initiative was “not worth the ink it was written with” and “the resistance will continue until all the demands of our people are met.”

Israel reported a rocket launched over southern Israel just after 10 a.m., though there was less fire than there has been in previous days.

The Hamas rejection came just minutes after Israel’s security cabinet met and decided to embrace terms set forward late Monday night by Egypt’s military-backed government. Egypt has been deeply hostile toward Hamas since last year, when a military-backed coup ousted the Muslim Brotherhood-aligned president, Mohamed Morsi, who had helped to negotiate a previous ceasefire between Israel and Hamas in late 2012.

Israeli defense official Amos Gilad told Israel Radio that Hamas had been significantly weakened by a week-long conflict that has claimed at least 185 lives in Gaza.

Palestinian Foreign Minister Riyad al-Malki speaks on his cellphone Monday before an extraordinary session of the Arab League in Cairo. Egypt launched an initiative on Monday to halt fighting between Israel and Palestinian militants. (Amr Abdallah Dalsh/Reuters)

“Look at the balance, and you see that Hamas tried every possible means of striking at Israel while bringing great and terrible damage on its people,” he said.

The Egyptian proposal appeared timed to greet the arrival of Secretary of State John F. Kerry, who is due in Cairo on Tuesday, according to the Israeli news media. A draft of the initiative did not include a detailed plan but called for a de-escalation by 9 a.m. Tuesday followed by a full truce within 12 hours of the proposal’s “unconditional acceptance” by both sides.

The White House, in response to questions about its role in cease-fire proposals, said the United States “has been deeply engaged in conversations with our partners throughout this difficult period, and we will continue doing everything we can to facilitate a return to the 2012 cease-fire.”

National Security Council spokesman Bernadette Meehan said: “We welcome Egypt’s call for a cease-fire and hope this will lead to the restoration of calm as soon as possible.”

As rumors of a cease-fire spread, people in Gaza remained wary. The beach villas were empty, the farms abandoned and the teeming street life in the northern tier of the Gaza Strip vanished as fleeing residents left ghost towns behind them.

The tens of thousands of panicked people who fled their homes in the northern Gaza Strip stayed far away, in shelters or with relatives in the south, after the Israeli military dropped leaflets Sunday warning that a new, more intense military operation was imminent.

Over the past seven days, Israel has hit more than 1,470 targets in Gaza. Its airstrikes have killed 185 people , including 38 children and 27 women, according to the Gaza health ministry. Another 1,390 were injured.

Hamas and other Islamist militant factions in Gaza have fired more than 1,000 rockets at Israel. Air raid sirens rang over Israel’s major cities, including Jerusalem and Tel Aviv, but the salvos caused only moderate damage and no fatalities .

The top Hamas leader in Gaza, Ismail Haniyeh, appeared to be preparing Palestinians for an end to the latest round of violence. In a televised address, he thanked the people of Gaza for their suffering and said, “The problem is not the cease-fire, the problem is the situation in Gaza.”

Haniyeh complained that Gaza was living under a state of siege, that the border crossing into Egypt has been closed, that salaries have not been paid and that Israel arrested hundreds of Hamas members in a military sweep in the West Bank last month that followed the abduction and murder of three Israeli teenagers.

Hamas has been promising “a surprise,” and on Monday it sent an unmanned aerial vehicle into Israeli airspace — a first. Israel shot down the drone as it passed over the southern Israeli city of Ashdod.

Hamas posted on the Internet images and video of another drone flying in the air, with the sea on its left wing and ground below. This drone had four small rockets or missiles under its wings.

Hamas said that its engineers have manufactured three types of unmanned aircraft, including ones that could be used to conduct surveillance, to fire weapons or to serve as a guided missile — a kind of “suicide” drone.

The claims of armed drones or overflights of Israeli military installations could not be independently confirmed.

But the first penetration of Israeli airspace by a Hamas drone may signal a new threat. Tal Inbar, a research leader at Israel’s Fisher Institute for Air and Space Strategic Studies, said that the drone showed in the Hamas video was an Iranian system with a wingspan of nearly 10 feet.

“You could smuggle it in a couple of crates,” Inbar said.

Karen DeYoung in Washington contributed to this report.