At Least 13 Israeli Soldiers, 87 Palestinians Killed In Gaza Strip Sunday

Updated at 10:30 p.m. ET.

A spokesman for Hamas claimed Sunday that the group has captured an Israeli soldier. Reuters quotes Israel's ambassador to the U.N., Ron Prosor, as saying that no Israeli soldier has been kidnapped.

It's the latest development in a bloody day of fighting between Israel and Hamas. Israel's military said today that a series of attacks on its forces inside the Gaza Strip has killed 13 soldiers, by far the heaviest single-day toll for its troops since the beginning of the offensive nearly two weeks ago.

Meanwhile, Secretary of State John Kerry will travel to Cairo Monday to help support efforts to broker a cease-fire, U.S. State Department spokeswoman Jen Psaki said in a statement Sunday.

According to Reuters, Hamas militants said they'd ambushed Israeli Defense Forces troops, setting off explosives around their vehicles. Other Islamist militants said they'd attacked Israeli soldiers in a Gaza house. The latest deaths bring to 20 the number of Israelis killed in the fighting — 18 soldiers and 2 civilians.

At least 425 Palestinians, including 111 children, have been killed since the fighting started. More than 3,000 have been wounded, according to Gaza Health Ministry spokesman Ashraf al-Kidra.

Israel says it is stepping up the ground war, sending more troops into Gaza and intensifying tank fire and airstrikes, NPR's Daniel Estrin tells our Newscast desk.

Earlier, however, Israel agreed to extend a brief "humanitarian truce," meant to allow both sides to tend to the wounded, to four hours, despite charging Hamas with breaking the halt in fighting by firing at its soldiers. A Hamas spokesman later said it was Israel that broke the truce with renewed use of artillery.

The temporary cease-fire was specifically aimed at treating the wounded in a northeastern Gaza neighborhood known as Shejaia after the IDF intensified shelling there, The Jerusalem Post reports.

Al-Kidra of Gaza's Health Ministry says 87 Palestinians have been killed in Sunday's fighting, 60 of them in Shejaia.

The news agency says the casualties in Shejaia are the heaviest since Israel launched its offensive on July 8 after cross-border rocket strikes by militants intensified.

According to Reuters:

"Palestinian President Mahmoud Abbas, who is based in the occupied West Bank, accused Israel of carrying out a massacre and declared three days of mourning.

"The Israeli military said on Sunday Hamas had deployed rockets and built tunnels and command centres in Shejaia. 'Two days ago, residents of Shejaia received recorded messages to evacuate the area in order to protect their lives,' an Israeli military spokeswoman said."

On NBC's Meet the Press, Kerry emphasized that Israel "has every right in the world to defend itself" from Hamas attacks.

Speaking on ABC's This Week, Kerry said: "It's ugly. War is ugly, and bad things are going to happen." He added that Hamas needs "to recognize their own responsibility." Hamas he said on CNN must "step up and show a level of reasonableness, and they need to accept the offer of a cease-fire."

U.N. Secretary-General Ban Ki-moon condemned Sunday's bloodshed, saying that "Israel must exercise maximum restraint.

"I repeat my demands to all sides that they must respect international humanitarian law. The violence must stop now," he said.