GAZA CITY (CNN) — Thirteen Israeli troops were killed overnight in Gaza, the Israel Defense Forces said Sunday.
The IDF did not immediately give details.
Hamas said it lured Israeli tanks into a Gaza field in which it had hidden improvised explosive devices, and "destroyed the force completely."
In a statement, Hamas claimed "responsibility for this heroic operation on the doorsteps of Gaza."
It was Israel's biggest death toll in the current fighting, bringing the total killed to 18 soldiers and two civilians.
Among Palestinians, the death toll has soared past 400.
Hundreds fled in panic into Gaza City on Sunday as Israeli troops focused their firepower on the nearby town of Shaja'ia. The shelling and bombing killed at least 60 people and wounded 300, according to the Gaza Health Ministry.
Bodies lay in streets beside gashes blasted into apartment buildings, said people who had escaped the violence.
Overnight, Hamas fired rockets from Shaja'ia toward Israel. The militant group also turned down an invitation by Egypt to talk about a cease-fire initiative that Cairo had proposed.
For three days, the IDF had warned residents of Shaja'ia to flee, Israel said. Such warnings are delivered through calls and text messages as well as fliers that said "it is the intention of the IDF to carry out aerial strikes against terror sites and operatives" in the area. The fliers told people to head to Gaza City by Wednesday morning and not to return until further notice. The IDF posted an English translation of the fliers Sunday on Twitter.
Some residents said they received the warnings but felt that even if they fled, they could face the same dangers in other parts of Gaza.
But the IDF said Hamas "ordered them to stay" and "put them in the line of fire."
The IDF posted a photo Sunday on Twitter, saying, "We fired a warning shot at this target in Gaza. In response, these civilians ran to the roof and brought their kids."
Militants have launched about 300 rockets into Israel since the beginning of Israel's ground operation, the IDF said. More than 200 hit Israel, and 64 were taken out by the Iron Dome defense system.
On Saturday, a rocket killed an Israeli in Negev and wounded four others, including an infant, Israeli authorities said.
At Barzilai Hospital in Ashkelon, soldiers have been coming in with serious wounds from shrapnel and gunshots. The hospital treats soldiers and civilians, as well as injured Palestinians, although none were there Sunday.
The hospital is frequently hit by rocket attacks from Gaza. It has emergency procedures in place, including moving its neo-natal ward into a reinforced rocket shelter.
Israel announced Sunday it would open a field hospital at the Erez Crossing to treat injured Palestinians. On Saturday, the defense forces delivered truckloads of medical supplies to Gaza.
Israel is still "early on in the mission," IDF spokesman Lt. Col. Peter Lerner said Sunday. "You can't erase 10,000 rockets overnight," he said of Hamas' arsenal.
The IDF is adding troops to the incursion. It called up tens of thousands of reservists at the start of Operation Protective Edge to prepare for the ground operations.
Israel said it has struck "2,300 terror targets" in Gaza and found 13 tunnels the militants use for smuggling weapons.
Since beginning ground operations Thursday, Israel said, it has killed at least 70 terrorists and captured others.
U.S. may dispatch Kerry
Secretary of State John Kerry told CNN Sunday he may travel to the region.
"I believe the President is asking me to go over there in very short order to work on the issue of a cease-fire," he told CNN's "State of the Union."
"Israel is under siege by a terrorist organization that has seen fit to dig tunnels and come through those tunnels with handcuffs and tranquilizer drugs, prepared to try to capture Israeli citizens and take them back to hold them hostage. No country could sit by and not take steps to try to deal with people who are sending thousands of rockets your way," Kerry said.
During one phone call with President Obama, Israeli Prime Minister Benjamin Netanyahu "had to interrupt the conversation with the President of the United States to go to a shelter. People can't live that way," Kerry said.
Obama spoke with Netanyahu again Sunday, White House spokesman Josh Earnest said.
The United States supports Egypt's initiative for a cease-fire and "will work for a fair cease-fire," Kerry told CNN. The United States has "shown our willingness to try to deal with the underlying issues," but Hamas "must step up and show a level of reasonableness," he said.
"No country, no human being, is comfortable with children being killed, with people being killed, but we're not comfortable with Israeli soldiers being killed either or with people being rocketed in Israel."
"Hamas uses civilians as shields," he said. "They fire from a home and draw the fire into the home."
Fawzi Barhoum, a spokesman for Hamas, said on Aqsa TV on Saturday that there would be no truce or surrender while Israel is attacking.
Israel agreed to a two-hour cease-fire Sunday, at the request of the Red Cross, to allow Palestinian emergency medical workers to tend to the wounded and dead in Shaja'ia, the IDF said. Israel also announced it was extending its cease-fire, but said Hamas was not holding its fire.
Hamas, meanwhile, said Israeli forces shelled Shaja'ia after the cease-fire was declared.
The IDF said it has held fire three times since beginning the operation in Gaza, but "Hamas never stopped shooting rockets."
Netanyahu: Demilitarize Gaza
Netanyahu called on the international community to "undertake a program to demilitarize Gaza" in the future.
The situation is "unacceptable" because of Hamas and Islamic Jihad, Netanyahu told CNN's Wolf Blitzer in an interview Sunday
"These people are the worst terrorists -- genocidal terrorists. They call for the destruction of Israel and they call for the killing of every Jew, wherever they can find them."
Hamas fighters in Gaza "don't care" about the dying people around them, Netanyahu said.
Israel has enabled the shipment of concrete into Gaza for buildings, hospitals, and schools, but the militants use hundreds of tons of it for each tunnel, Netanyahu said.
Hamas spokesman: Israel committed "crime against humanity"
Hamas spokesman Sami Abu Zuhri, speaking to Al-Jazeera, said Israel committed "a crime against humanity," and that most of those killed in Shaja'ia were women and children. "Our people will not sit idle in front of this brutal aggression."
He called on the Palestinian Authority, in the West Bank, to "stop its security coordination with the occupation" and to "stop suppressing the demonstrations in the West Bank." He also said "the Arab world should not sit idle."
The Israeli government has repeatedly said that, unlike Palestinian militants, the IDF does not target civilians and works to avoid innocent casualties.
But in Gaza, one of the most densely populated areas on Earth, more than 70% of those killed in the hail of artillery and airstrikes have been civilians, according to the United Nations. A fifth were children. More than 40% of Gaza's population is 14 years old or younger.
About 81,000 Palestinians have taken refuge in U.N. facilities, Robert Turner, the director of U.N. efforts in Gaza, said Sunday. The United Nations has been investigating a cache of rockets used by militants found in a U.N. school.
Leaders from the United States and Europe last week expressed public support for Israel's right to defend itself against missiles from Gaza.
CNN's Ben Wedeman and Karl Penhaul reported from Gaza; CNN's Ben Brumfield and Josh Levs from Atlanta. CNN's Atika Shubert reported from Israel near Gaza. CNN's MIchael Martinez, Kareem Khadder, Ian Lee, Ali Younes, Ralph Ellis, Tim Lister, Samira Said, Michael Schwartz, Salma Abdelaziz and Tal Heinrich contributed to this report.
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