(CNN Newsource) Israel said it killed Hamas militants who entered the country Monday, while officials in Gaza said Israel shelled a hospital, killing several people. The latest violence, on the heels of the conflict's bloodiest day, came as the United States and world powers stepped up their push for a cease-fire.?The Shuhada Al-Aqsa hospital in central Gaza was hit by shelling, leaving four people dead, the Gaza Health Ministry said. Hamas TV showed upper floors damaged.
Israel, meanwhile, killed more than 10 Hamas terrorists who entered the country through tunnels "to attack two different kibbutzim," or communal areas, "where farmers are trying to conduct their daily lives," government spokesman Mark Regev told CNN.
The death toll among Palestinians has passed 500. The biggest assault so far took place Sunday in the town of Shaja'ia.
On the Israeli side, where the Iron Dome defense system helps protect people against missile attacks every day, the death toll stands at 20 -- 18 soldiers and two civilians. Thirteen of the soldiers were killed Sunday in a Hamas attack. Two were Americans: California native Max Steinberg and Sean Carmeli, from South Padre Island, Texas, the U.S. State Department said.
"We will see Hamas come out of this substantially weakened, their arsenal of dangerous weapons diminished," Regev vowed Monday in an interview with CNN's Wolf Blitzer. "They will understand they can't shoot at our people with impunity."
But Palestinian leaders paint a very different picture. "Israeli massacres in Gaza result in mass civilian killings," official news agency WAFA, run by the Palestinian government in the West Bank, reported Monday. "At least 515 Palestinians have been killed," the news agency said.
It's unclear how many of the dead in Gaza were militants. The United Nations has estimated that 70% were civilians. Israel has reported that dozens of terrorists were killed in Gaza.
Israel blames Hamas for civilian deaths in Gaza, noting that the group has encouraged people to stay in their homes despite repeated warnings from Israel in advance of airstrikes. But some Palestinians have said they feared that even if they left they could face the same violence anywhere in Gaza. More than 83,000 Palestinians have taken refuge in U.N. facilities.
"Nobody is safe and nobody can flee anywhere because everywhere is targeted," said Enas Sisisalem, a mother of two who lives in the al-Remal neighborhood of Gaza City. "When we hear the shelling my kids will cry."
In a meeting late Sunday, U.N. Security Council members expressed "serious concern about the growing number of casualties," according to the body's president, Ambassador Eugene-Richard Gasana of Rwanda.
The members urged "an immediate cessation of hostilities" based on the cease-fire that stopped the 2012 conflict between Israel and Hamas, he said.
Israeli soldier captured?
Hamas said Sunday it had captured an Israeli soldier. "He is a prisoner, and if Zionists lie about the dead and wounded, then the fate of this soldier is their responsibility," Hamas spokesman Abu Obeida said.
Gunfire and cheers erupted in Gaza in apparent celebration of the soldier's capture.
Israel's ambassador to the United Nations later disputed that claim. "There's no kidnapped Israeli soldier, and those rumors are untrue," Ron Prosor said.
But Monday morning, the Israeli government said it was unsure.
"It could just be Hamas bravado. We're looking into it," Regev said. "We don't underestimate Hamas. Hamas has built a formidable military machine. We see that with these rockets that they can shoot at the center of our country -- at Jerusalem and Tel Aviv. That network of tunnels under the Gaza Strip, there's a whole subterranean terror world there in Gaza. Some of those can go into Israel and pop up on our side of the frontier with arms, with explosives and can cause murder and mayhem on our side. So we take the Hamas threat very seriously."
If the claim is true, it will be "a game changer immediately because it's going to change what the Israelis are doing on the ground in that sector. They're going to be looking for him," said CNN military analyst Lt. Col. Rick Francona. But, he added, "overall, the Israeli strategy is not going to change. They're committed to this mission."
In 2006, Israeli soldier Gilad Shalit was captured. He was released some five years later in exchange for more than 1,000 Palestinian prisoners.
After hot mic comments, Kerry heads to region
U.S. Secretary of State John Kerry is due to arrive in Egypt on Monday to push for a cease-fire.
Speaking to CNN's "State of the Union" on Sunday, Kerry said that the United States supports Egypt's initiative for a truce. 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," Kerry said.
While his public comments were steadfastly supportive of Israel, Kerry appeared to let slip some frustration with Israel in comments caught on an open microphone between television interviews.
After one of his deputies mentioned the latest number of Palestinian casualties, Kerry was heard to say, "It's a hell of a pinpoint operation."
U.S. President Barack Obama spoke Sunday with Israeli Prime Minister Benjamin Netanyahu, the second call in three days. Obama reiterated U.S. condemnation of Hamas attacks against Israel "and reaffirmed Israel's right to defend itself," the White House said in a statement. Obama also "raised serious concern about the growing number of casualties, including increasing Palestinian civilian deaths in Gaza and the loss of Israeli soldiers."
Regev said Israel supports the Egyptian initiative for a cease-fire.
Hezbollah reaches out to Hamas
The Lebanese militant group Hezbollah reached out to Hamas to express its support Monday.
Hassan Nasrallah, the group's secretary-general, spoke with Hamas political chief Khaled Meshaal, who lives in Qatar.
Nasrallah "praised the steadfastness of the resisters and their creativeness in the battlefield, the enormous patience of the wronged people of Gaza and their stand behind their resistance," according to a CNN translation of a Hezbollah statement.
Nasrallah also spoke with Ramadan Shallah, head of Islamic Jihad, another Palestinian militant group, the statement said. Shallah is one of the FBI's most wanted terrorists.
CNN's Karl Penhaul and Ian Lee reported from Gaza City, Josh Levs from Atlanta and Jethro Mullen from Hong Kong. CNN's Kareem Khadder, Ben Wedeman, Atika Shubert, Ben Brumfield, Tim Lister, Michael Martinez, Mohammed Tawfeeq and Yon Pomrenze contributed to this report.
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