JERUSALEM — Four Israeli soldiers and 10 Palestinian militants were killed inside Israeli territory Monday morning, Israeli military officials said, after armed gunmen from the Gaza Strip managed to infiltrate through two more of the tunnels that Israel says its ground operation is targeting.
As diplomatic pressure for a cease-fire mounted on the conflict's 14th day, the Palestinian death toll topped 500 and the number of Israeli soldiers killed hit 25, more than twice as many as in Israel's last Gaza ground operation in 2009. Two Israeli civilians have also died from rocket and mortar fire.
The military provided few details about the incursions into Israel, outside Gaza's northeast corner, saying only that "two terror squads were detected." An airstrike targeted one group of militants, the statement said, and "soldiers who were called to the scene" engaged the other.
The military released video footage showing several masked gunmen in bushes that it said were about a half-mile from the Israeli border town of Sderot, and an explosion that targeted them as they retreated into the tunnel. Three other Israeli soldiers were killed in battles inside Gaza on Monday.
Ismail Haniya, until recently the Hamas prime minister, said in a speech broadcast from Gaza that the fighting would continue unless an agreement met the movement's demands: opening crossings, lifting restrictions on fishing, farming, import and export, and releasing prisoners who were freed in a 2011 exchange for an abducted Israeli soldier and recently rearrested.
"We'll never go back to the period before the aggression, we'll never go back to the slow death," Haniya said in an address laden with Koranic verses. "Gaza will be the graveyard for the invaders, as it always was in the history."
In Gaza, the United Nations reported nearly 100,000 people in 67 shelters, as an airlift of 45,000 mattresses and 10,000 blankets was en route from Dubai.
As the Palestinian death toll has climbed over two weeks, thousands of people streamed toward Gaza City from the north on foot, in donkey carts and packed into cars. The Israelis seemed to be stepping up artillery shelling in the central Gaza refugee camps El Bureij and El Mughazi, where they had earlier urged people to evacuate.
Hamas radio reported that four people were killed in a strike on Al Aqsa Martyrs Hospital in El Bureij.
Knots of 10 to 12 people were hurrying with plastic bags of belongings across the main road, Salahadin Street, where a shell hit next to a car full of international journalists, spraying shrapnel on the roof. Hazem Abu Ghaben, who lives in El Mughazi, said he had gone to a relative's house over the weekend, returned home because he thought things had calmed down, then regretted it and was fleeing anew.
The situation had gotten "a million times worse," Abu Ghaben said.
At the Abu Jamei family's home near the southern town of Khan Younis, people searching beneath the rubble left by an overnight attack Monday counted 26 bodies, by far the most victims of a single strike in this offensive. In the southern border town of Rafah, artillery shelling of homes belonging to the Siam family killed 11 people, witnesses said, including three children.
Rocket fire from Gaza slowed somewhat from earlier days, but more than a dozen sirens sounded around midday. One rocket hit a home in Sderot, near Gaza, while the occupants cowered in a safe room. Another rocket landed in an open field near Tel Aviv.
Across Israel, funerals were scheduled for at least five soldiers from the decorated Golani Brigade who were killed in Shejaiya on Sunday. The military said it had still not determined whether a soldier had indeed been captured alive, as Hamas claimed in a statement Sunday night. The Israeli military announced that two of the dead were among the hundreds of Americans in the Israeli army: Max Steinberg, 24, from Southern California and Nissim Sean Carmeli, who grew up in Texas but finished high school in Israel.
The new underground incursions highlighted a dilemma for Israel's leadership, which has tried to build international support for its ground operation by saying it was a limited one focused on the tunnel threat, and by embracing cease-fire proposals from Egypt. Now, with President Barack Obama dispatching Secretary of State John Kerry to Cairo to seek an immediate halt to hostilities, Israel may be pressured to leave the tunnel mission unfinished in order to restore quiet.
Dan Shapiro, the U.S. ambassador to Israel, said Monday that Kerry would be working with Egyptians, Israelis and leaders of the Palestinian Authority to "bring back the quiet" that followed a 2012 agreement ending eight days of cross-border violence. In an interview on Israel Radio, Shapiro said Washington supported "Israel's right to protect itself" and "understood the need" to destroy tunnels but was "also worried about the number of dead and injured."
"Start with a cease-fire," he said, "and only after hold discussions on the problems at the base of the crisis."
But Gilad Erdan, a right-wing member of Israel's so-called security cabinet, which makes strategic decisions, said Israel "must not agree to any proposal for a cease-fire until the tunnels are eliminated," according to the Israeli news site Ynet. Speaking after he visited wounded soldiers at Barzilai hospital, Erdan raised the specter of a reoccupation of Gaza, saying "a green light has been given to expanding the action, and we should consider leaving forces in the northern part of the Gaza Strip to deal with the tunnels at the end of the operation."
Tzipi Livni, Israel's justice minister and representative to the U.S.-sponsored peace negotiations with the Palestinians that collapsed in April, said "demilitarization of Gaza" was essential but was "something we will discuss with the international community the day after."
"Now we are focused on the need to stop these terrorists, to act against these tunnels, and to stop these rockets against Israel," Livni said in a conference call with international journalists that was interrupted by sirens signaling incoming rockets from Gaza overhead. "The whole idea of the proposal is to cease the fire, stop the fire. This is the main goal right now."
Noting that Ban Ki-moon, the secretary-general of the U.N., was headed to Cairo as well as Kerry, she added, "These days are, I believe, crucial days."