GAZA CITY, Gaza Strip — The conflict in Gaza raged on Sunday, even as both Israel and Hamas offered brief truces and President Obama pressed Israel for an “immediate, unconditional humanitarian cease-fire,” reflecting growing concern over the rising death toll.

Israel denied Sunday that it was responsible for one of the most shocking attacks in the 20-day conflict, saying its soldiers were not behind the deaths of 16 Palestinians killed by shelling three days earlier as they sought refuge in a U.N. school near an area of intense fighting.

Israel’s military, however, offered no details about what it called a “comprehensive inquiry” into the incident. It released a grainy, 26-second aerial video showing what the military called an “errant” mortar landing in an empty courtyard of the school as proof that it didn’t kill anyone.

The U.N. Relief and Works Agency, which used the school as a shelter for Palestinians fleeing the violence, did not accept Israel’s conclusion. Spokesman Christopher Gunness called for an investigation that would be “fair and objective.”

In a telephone conversation with Israeli Prime Minister Benjamin Netanyahu on Sunday, Obama reaffirmed Israel’s right to defend itself and condemned Hamas attacks, the White House said in a statement.

But as the administration continued trying to balance its support for Israel with criticism of civilian casualties in Gaza, Obama also urged an immediate humanitarian cease-fire. He expressed “the United States’ serious and growing concern about the rising number of Palestinian civilian deaths and the loss of Israeli lives.”

The current conflict has killed more than 1,035 Palestinians, more than 70 percent of them civilians, according to the United Nations. Israel has lost 43 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 within Israel.

Netanyahu, in appearances on American Sunday-morning talk shows, signaled that he planned to keep targeting Palestinian militants and destroying Hamas tunnel networks, through which the fighters have sought to infiltrate Israel.

“Israel is not obliged and is not going to let a terrorist organization determine when it’s convenient for them to fire at our cities, at our people, and when it’s not,” Netanyahu said on “Fox News Sunday.” “We’ll take the necessary action to protect our people, including, by the way, continuing to dismantle tunnels. That’s our policy.”

Israel resumed airstrikes in the Gaza Strip midmorning Sunday, after offering Saturday night to extend a humanitarian cease-fire that had halted fighting in the coastal strip for 12 hours. But Hamas rejected the Israeli offer to extend the truce for 24 hours. Rockets flew from Gaza into Israel throughout the morning, with six reaching Tel Aviv. Israeli artillery and airstrikes pounded parts of Gaza.

By the afternoon, Hamas had announced its own 24-hour humanitarian truce, beginning at 2 p.m. local time, to allow Palestinians to prepare for the three-day Eid al-Fitr holiday, which caps the Muslim fasting month of Ramadan. But Lt. Col. Peter Lerner, a spokesman for the Israeli army, said that the military had not received any official order to stop its operations in Gaza and that Palestinian militant rockets continued to soar into Israel past 2 p.m.

Shortly before 1 p.m. Sunday, an Israeli airstrike hit a large, empty house in Gaza City’s eastern neighborhood of Shijaiyah, the site of fierce clashes a week ago. Three people were killed and at least two were injured, according to witnesses.

Neighbors said the Mortaja family, who owned the house, are not militants but merchants who sell fishing supplies. The people who were killed, residents said, were walking past the house when it was struck and collapsed into a mass of concrete and tangled metal.

“If we had any suspicions about the house or the family, we would have left the area,” said Abu Ahmed, 66, a neighbor.

Just after 6 p.m., an artillery shell crashed into another part of the neighborhood, sailing in from the direction of the border with Israel, where Israeli forces are positioned. Within 15 minutes, two more shells followed.

“Can you hear? Can you hear? They are shelling now,” declared Muhammad Sawah, 20. “We can’t trust the Israelis.”

Sunday night, Israel said it had attacked 40 militant targets, including rocket launchers and a tunnel, since resuming firing on Gaza in the morning. The military reported that 72 rockets were launched at Israel from Gaza on Sunday, with 51 hitting Israeli territory and nine intercepted by Israel’s Iron Dome missile-defense system. The others were duds or fell short.

Israel has said that its military does not target schools or U.N. shelters. The military video it released Sunday left unanswered many questions about the attack on the school; it did not show what happened after the mortar landed. It was not clear whether shrapnel from the explosive might have hit people hiding in the school’s corridors or classrooms.

“We informed the Israeli Army of the location of this designated UN shelter, clearly marked with a UN flag,” Gunness said in a statement. He added that the organization had “made numerous phone calls to the Israeli army requesting a pause for the evacuation of civilians but that request was never granted.”

Israel has denied the allegations.

Hamas spokesman Sami Abu Zuhri denied Israel’s suggestion that Hamas mortars or rockets could have caused the casualties at the school. He noted that witnesses and the United Nations have alleged that Israel was responsible. “Israel is the accused party, and they don’t have the right to investigate and to press charges,” Zuhri said Sunday.

In the center of Gaza City on Sunday, thousands of Palestinians emerged from their houses to purchase salted fish, meat and gifts to celebrate Eid. Others waited in long lines at the local Western Union office, which had closed during most of the clashes, to receive money from relatives.

Maher Abu Sido, 52, got $700 from his brother in Dubai, funds he had been awaiting for more than a month. He said he would use it to buy food for his 10-member family. He expects the money to last a month, he said.

“It’s Eid, so Palestinians from everywhere are sending money to help their relatives,” said Rami Al-Arouki, deputy manager of the Western Union office.

Still, many Gazans said Eid will be bittersweet this year because of the numerous Palestinian casualties. Celebrations are expected to be muted, and Gazans said that instead of buying gifts, they would help displaced families.

“The martyrs are our Eid,” said Ahmed Al-Rifi, 38, as he waited in a line to use an ATM.

Only subscribers are eligible to post comments. Please subscribe or to participate in the conversation. Here’s why.

Use the form below to reset your password. When you've submitted your account email, we will send an email with a reset code.