Israel will press its air and ground offensive in the Gaza Strip, Prime Minister Benjamin Netanyahu said Monday, preparing his country for a longer and bloodier campaign and dashing hopes that the three-week-old conflict would end soon.

Rebuffing appeals from President Obama, the United Nations and others for an immediate cease-fire, Netanyahu said in a televised address, “We will not finish the mission, we will not finish the operation, without neutralizing the tunnels” through which Hamas fighters have sought to infiltrate Israel. The tunnels, he said, “have the sole purpose of destroying our citizens, killing our children.”

Israel’s antagonist, the Islamist militant organization Hamas, which controls the Gaza Strip, continued to unleash deadly mortar and rocket fire, triggering air raid sirens across Israel.

In Gaza City, explosions Monday rocked a neighborhood and left at least 10 people dead, including children playing on a street, as a brief lull on one of Islam’s holiest days gave way to fresh attacks and tragedy.

Palestinian health officials said the deaths were among 18 reported in Gaza on Monday, the start of the Muslim Eid al-Fitr holiday capping the end of the fasting month of Ramadan. They said 70 people were injured.

Satellite images released by the United Nations show the impact of Israeli strikes on structures in Gaza. One of the most ravaged areas is the Shijaiyah neighborhood in the southeastern part of Gaza City.

Hamas officials blamed Israeli airstrikes for the blasts at the al-Shati camp, also called Beach Camp. A spokesman for the Israel Defense Forces denied firing at the neighborhood and attributed the explosions to failed rocket launches from Gaza militants.

Reporters said that a shell or rocket also crashed into a medical facility in the Shifa Hospital compound in Gaza City but that there was no serious damage and that it was unclear whether there were any deaths or injuries from that strike. Hamas and the Israeli military each denied responsibility for the blast.

In a text message to journalists, Hamas spokesman Sami Abu Zuhri called the strike on Beach Camp “a massacre” and vowed that “this crime will not break our will, and the occupation will pay a price.”

Later, Hamas militants fired three rockets into southern Israel, as revenge, they said.

Early Tuesday morning, Israeli military said that five soldiers were killed Monday evening when militants from Gaza infiltrated southern Israel via a tunnel from the Gaza Strip. A gunfight broke out, leaving at least one militant dead, as well as five soldiers, bringing to 10 the total number of soldiers killed in combat Monday.

Early Tuesday, an Israeli aircraft fired a missile at the house of Ismail Haniyeh, the former Hamas prime minister of Gaza, causing damage but no casualties, Reuters reported, citing Gaza’s Interior Ministry. An Israeli military spokeswoman had no information on the report but was checking for details. Haniyeh’s son said on his Facebook page that the house was empty.

Hamas said that its al-Aqsa TV station was also targeted but that the station continued to broadcast.

Children paying a terrible price in Gaza

The latest bloodshed occurred as international efforts to end the devastating war had been intensifying. Early Monday, the U.N. Security Council called for an “immediate and unconditional humanitarian cease-fire.”

The conflict has killed more than 1,060 people in Gaza, more than 70 percent of them civilians, according to the United Nations. Israel has lost 53 soldiers, the largest toll since its 2006 war with Lebanon. Hamas mortar and rocket attacks from Gaza have killed two Israeli civilians and a Thai worker in Israel.

At Shifa Hospital, the best-equipped in the coastal enclave, chaotic scenes unfolded as the dead and the wounded arrived, some by ambulance, some carried in the arms of relatives. One woman was shaking uncontrollably and screaming, “My brother, my brother!” One man was crying in front of the mangled corpse of his father.

Naji al-Deen was seated on a chair, staring blankly, his clothes covered in blood.

Like hundreds who had come to the hospital, he was from the al-Shati camp, a seaside neighborhood filled with the families of refugees from the 1948 war that created the Israeli state. On Monday, it was a death zone. Children had been playing on a portable swing set brought in to celebrate the holiday, as well as in the narrow, tree-lined street, witnesses said. About 4:30 p.m., the blast occurred.

“It was Eid, and the children wanted to play,” said Deen, his voice cracking. “Then we heard the explosion. I saw my son running covered in blood. There were kids torn to pieces.”

Deen said he carried his son to the hospital, where he was being treated for his injuries. At least seven children were killed, witnesses said.

There were signs of rising hostilities Monday evening. Israeli media reported that militants had sneaked into southern Israel via a tunnel. The reports said that there was an exchange of fire and that five militants were killed.

Sirens sounded across southern, central and northern Israel, warning people to seek shelter from incoming Gaza rockets.

The Israeli military made cellphone calls and sent text messages to thousands of Palestinians living in the Shijaiyah, Zeitoun and Jabalya neighborhoods, warning them to evacuate immediately and head for Gaza City. Similar mass messages have preceded large strikes and incursions by Israel recently.

“If the terrorist organizations in Gaza think they can break Israel and its citizens, they will come to understand in the next few days that this is not the case,” said Israeli Defense Minister Moshe Yaalon.

The day started quietly, with many Palestinians hoping to celebrate Eid al-Fitr, typically a joyous time of parties. Israel mostly held its fire overnight, shelling only a site in the northern Gaza Strip in response to rocket fire there. But it turned out to be the briefest of respites in Gaza.

In an emergency meeting that stretched into early Monday, the U.N. Security Council urged Israel and Hamas to “accept and fully implement the humanitarian cease-fire into the Eid period and beyond,” allowing for the delivery of urgently needed assistance to Palestinians, who cannot leave the territory.

U.N. Secretary-General Ban Ki-moon again appealed to Israel and Hamas to end the bloodshed.

Netanyahu heaped scorn on the U.N. statement, saying it focused on “the needs of a murderous terrorist organization that is attacking Israeli civilians and does not address Israel’s security needs, including the demilitarization of the Gaza Strip.”

In a telephone conversation, Netanyahu told Ban that the United Nations had ignored Hamas attacks on Israeli civilians and the group’s use of civilians as human shields.

On Sunday, Obama had also urged an immediate humanitarian cease-fire, according to the White House.

In Washington on Monday, U.S. officials confirmed that Israeli authorities had detained a 15-year-old American citizen for allegedly taking part in violent protests in East Jerusalem this month. State Department spokeswoman Jen Psaki said the U.S. government was urging a quick resolution of the case of Mohamed Abu Nie, arrested July 3. Israeli officials alleged that he had a knife and threw rocks and attacked police during a protest, Psaki said. She added that the U.S. government was concerned about reports that he had been beaten while in custody.

Raghavan reported from Gaza.