GAZA CITY, Gaza Strip -- Thousands of Palestinian residents of the northern Gaza Strip fled their homes on Sunday and sought safety in United Nations shelters, heeding warnings from the Israeli military about impending plans to bomb the area in the sixth day of an offensive against Hamas that has killed more than 160 people.

The fighting showed no signs of slowing, despite international calls for a cease-fire and growing concerns about the mounting civilian death toll in Gaza. U.S. Secretary of State John Kerry spoke to Israeli Prime Minister Benjamin Netanyahu and voiced U.S. "readiness" to help restore calm, while Egypt, a key mediator between Israel and Hamas, continued to work behind the scenes.

U.N. Secretary-General Ban Ki-moon called for an immediate cease-fire in a statement issued late Sunday by his spokesman's office.

Ban "strongly believes that it is in the interest of both sides that steps toward dangerous escalation be replaced with immediate measures to end the fighting, thus preventing further casualties and greater risks to regional peace and security," it said.

Ban condemned Hamas' indiscriminate firing of rockets on Israeli civilian targets as "a violation of international law," it said. He abhorred "the image of Israeli families hovering in shelters in fear of their children's safety" and demanded "an immediate cessation of these indecent attacks."

At the same time, the U.N. chief is "deeply worried about the impact on Palestinian families of Israeli military action. Too many Palestinian civilians have been killed, and any Israeli ground offensive will undoubtedly increase the death toll and exacerbate civilian suffering in the Gaza Strip," Ban's statement said.

Ban noted that despite the U.N. Security Council's demand for a cease-fire, "the situation in and around the Gaza Strip appears to be worsening."

Amid the diplomacy, Israel said it was pushing forward with preparations for a possible ground invasion of Gaza. Thousands of troops have massed along the border in recent days.

"We don't know when the operation will end," Netanyahu told his Cabinet on Sunday. "It might take a long time." He said the military was prepared "for all possibilities."

There seems to be little appetite for a return to the cease-fire of November 2012, which lasted little over a year and a half. Yuval Steinitz, the minister for strategic affairs, told Israel Radio that the immediate goal is "quiet," but "the strategic goal is demilitarization." He added, "We have to finally not be satisfied with a temporary filling, but do a root canal."

Israel launched the offensive last Tuesday in what it said was a response to heavy rocket fire out of Hamas-controlled Gaza. The military says it has launched more than 1,300 airstrikes, while Palestinian militants have launched more than 800 rockets at Israel.

One of Hamas' rockets on Sunday hit an Israeli power facility that supplies Gaza, cutting electricity to 70,000 Palestinians in the territory, the Israeli military said in a text message.

On Sunday night, Israel's military said rockets were fired at Israel separately from Syria and Lebanon. There were no injuries or damage, but Israel fears militant groups along its northern frontier may try to open a second front. The rocket attacks were the second such barrage on Israel from its northern neighbors in recent days.

The Israeli military said it retaliated by shooting toward the source of fire.

In Egypt, security officials said they had foiled a new attempt to fire rockets at Israel by militants in the northern Sinai Peninsula, which borders Israel.

The Palestinian Health Ministry in Gaza says 166 people have been killed, including dozens of civilians, and more than 1,000 hurt.

The violence is straining the Palestinian health system, and the World Health Organization appealed for $60 million to help prevent its collapse. Deputy Prime Minister Ziad Abu Omar and Health Minister Jawad Awad will head to Gaza for the first time since the Palestinians formed a Hamas-backed government in June, according to a government statement.

There have been no Israeli fatalities, though several people have been wounded, including a teenage boy who was seriously injured by rocket shrapnel Sunday.

Ground attack

Early Sunday, the Israeli air force dropped leaflets around the northern Gaza town of Beit Lahia ordering people to evacuate their homes. Israel says much of the rocket fire has come from the area, and overnight Sunday, the military carried out a brief ground operation on what it said was a rocket-launching site that could not be struck from the air. Four Israeli soldiers were lightly wounded before returning to Israel.

The U.N. refugee agency for Palestinians, UNRWA, said some 17,000 Palestinians had headed to special shelters set up in 20 U.N. schools in Gaza.

"The fact that in a span of almost a few hours, 10,000 people sought refuge in these 15 schools is an indication to the difficult situation on the ground," said Sami Mshasha, a UNRWA spokesman.

Some raced by in pickups, waving white flags. "Once we received the message, we felt scared to stay in our homes. We want to leave," said one resident, Mohammed Abu Halemah.

Shortly before nightfall, Israel carried out a series of airstrikes in Beit Lahia. Hamas' Al-Aqsa TV station reported four airstrikes in a 10-minute span, and a large plume of black smoke could be seen over the area from the Israeli border. There were no immediate reports of casualties.

Hamas, an Islamic militant group sworn to Israel's destruction, has remained defiant, and it continued to fire rockets into Israel throughout the day. It urged people in northern Gaza to stay in their homes and has so far rejected proposals for a cease-fire as unsatisfactory.

"They want us to put down our arms and leave the resistance," said Moussa Abu Marzouk, a top Hamas official, on his Facebook page. "They started the battle, and we will stay on our land and fight to protect our future."

Despite Israeli claims that it has inflicted heavy damage on the group, Hamas says it is largely unscathed, and Palestinian medics say most of the dead have been civilians.

The outbreak of violence follows the kidnappings and killings of three Israeli teenagers in the West Bank, the kidnapping and killing of a Palestinian teenager in an apparent revenge attack, and wide-ranging Israeli moves against Hamas militants and infrastructure in the West Bank. Hamas has demanded that hundreds of recently arrested activists be freed as part of a cease-fire.

Many of the airstrikes have been on the homes of wanted Hamas militants, putting their families at risk. In an attack on Saturday, the target of one such airstrike, Gaza's police chief, survived, while 17 members of his extended family were killed.

Local officials and relatives searched Sunday for more bodies before burying the family and a neighbor in a row of 18 graves dug in the same compound.

Israel accuses Hamas of using Gaza's civilians as human shields, putting people in the densely populated territory in danger.

"The leadership of Hamas and the other organizations has chosen -- at a time when they are using the population of Gaza as human shields -- to hide underground, to flee abroad and to deliberately put civilians in the line of fire," Netanyahu said.

Civilian toll mounts

Despite Israel's claims, the international community, including many of Israel's allies, have begun to express concerns about the growing civilian death toll.

In Vienna, Kerry spoke Sunday with Netanyahu over the phone and highlighted U.S. concerns about the "escalating tensions," the U.S. State Department said.

Kerry "described his engagement with leaders in the region to help to stop the rocket fire so calm can be restored and civilian casualties prevented, and underscored the United States' readiness to facilitate a cessation of hostilities," the State Department said.

Netanyahu's office declined comment on diplomatic efforts.

Egypt, meanwhile, said President Abdel Fattah el-Sissi spoke to Ban. El-Sissi's spokesman quoted Ban as praising Egyptian efforts to halt the fighting and affirming that "Egypt is the most capable party to effectively participate in reaching a calm between the two sides."

Other countries were also involved. Germany's foreign minister said he would head to the region today, while French President Francois Hollande tried to rally Arab and Muslim leaders to push for a cease-fire.

Hollande held telephone talks over the weekend with Turkish Prime Minister Recep Tayyip Erdogan and Tunisian President Moncef Marzouki.

Marzouki spokesman Adnane Mancer said the French and Tunisian presidents agreed that Marzouki would try to talk to Hamas leaders and urge a cease-fire, while Hollande would try to do the same with other parties. A French presidential official said Hollande was talking to Israeli, Palestinian and other Arab officials.

In Paris on Sunday, pro-Palestinian protesters tried to force their way into a synagogue with bats and chairs, then fought with security officers who blocked their way, according to police and a witness.

Sunday's unrest by a few dozen people came at the end of a peaceful protest of some 10,000 people in the French capital demanding an end to Israeli strikes on Gaza and accusing Western leaders of not doing enough to stop them.

Prime Minister Manuel Valls said two Paris synagogues had been targeted by unspecified violence that he called "inadmissible." In a statement, he said, "France will never tolerate using violent words or acts to import the Israeli-Palestinian conflict on our soil."

Back in Gaza on Sunday, Palestinians with foreign passports began leaving through the Erez border crossing. Israel, which cooperated in the evacuation, said 800 Palestinians living in Gaza have passports from countries including Australia, Britain and the U.S.

Rawan Mohanna, a 21-year-old chemistry major at the University of Texas, said she had arrived in Gaza with her family a month ago because her older sister was getting married to a Gazan.

Mohanna, who lives in Dallas, said her family is now returning to the U.S. with mixed feelings because her newlywed sister and other relatives were staying behind.

"It's bittersweet that we get to leave, but they are still there and they can't get out," she said.

Information for this article was contributed by Karin Laub, Josef Federman, Angela Charlton, Kirsten Grieshaber, Ian Deitch, Yousur Alhlou, Ibrahim Barzak, Sylvie Corbet and Mohammed Daraghmeh of The Associated Press; by Jonathan Ferziger, Alisa Odenheimer, Zainab Fattah, Yaacov Benmeleh and Saud Abu Ramadan of Bloomberg News; and by Steven Erlanger, Isabel Kershner, Fares Akram, Kareem Fahim and Merna Thomas of The New York Times.

A Section on 07/14/2014