Jerusalem (CNN) -- Despite calls for a new cease-fire, fighting intensified in Gaza on Monday and Tuesday morning, with Palestinians saying more than two dozen people died as rockets or mortars struck a refugee camp, a hospital and the center of Gaza City.
Eighteen people died as powerful and continuous air strikes rained down on Gaza City early Tuesday morning, the Palestinian Health Authority reported. And the Israeli military reported that 10 of its soldiers were killed Monday.
Al Aqsa TV reported that Israeli strikes hit the Ministry of Finance in western Gaza and the house of Ismail Haniyeh, a senior political leader of Hamas. A radio station run by Hamas was bombed.
Ten people, including eight children, were killed Monday when shells hit a refugee camp near the beach in Gaza where parents went to celebrate Eid al-Fitr, a Muslim holiday that marks the end of the holy month of Ramadan, the Gaza Health Ministry said.
The children were playing in the street near their homes when an explosion shook the ground. Holes as large as fists pockmarked a nearby building, and 10 people -- eight of them children -- were killed, according to Gaza's Health Ministry.
In the chaos, they were rushed to nearby Shifa Hospital. A TV news outlet run by Hamas showed live footage of the hospital. The channel blamed the carnage on an Israeli drone.
Shifa Hospital had been hit, too. Two people there were injured, the ministry said.
As before, Israel and Hamas accused each other of sending the bombs that killed people in Gaza. A short time later, Israel sent a text message to the media blaming Gaza "terrorists" for the attacks.
"In the blink of an eye," a father said, "I found body parts and heads cut off, no arms, no legs. I started to collect limbs, heads I couldn't recognize, I couldn't recognize my own children."
Though world leaders pleaded for a humanitarian cease-fire, Israeli Prime Minister Benjamin Netanyahu sent a message on Israeli television Monday.
"We need to be prepared for a protracted campaign in Gaza," he said.
Calling life under the threat of death "inconceivable" for Israel, Netanyahu said the military will not end its incursion into Gaza until it has destroyed tunnels Hamas is using to attack civilians outside Gaza.
Defense Minister Moshe Yaalon said Israel will not negotiate while Hamas is still attacking. "We will not hesitate to expand our operation," he said.
Deaths in Israel, too
Ten Israeli soldiers were killed Monday, according to the Israel Defense Forces.
Five were killed fighting militants who tried to attack Israeli civilians using a tunnel shaft leading to the Nahal Oz community, the IDF said. Israeli soldiers stopped the attempted attack, killing one of the attackers, the military said.
One Israeli soldier died in combat in southern Gaza. And another four were killed and eight were injured by mortar fire near Beeri, close to the Israeli-Gaza border, the IDF said.
Ashraf al-Qudra, spokesman for Gaza health ministry, said 1,101 people have been killed and more than 6,500 wounded in Gaza since the current conflict began. A total of 53 Israeli soldiers have died.
A central goal of Israel's military is to destroy tunnels that Hamas uses to smuggle weapons and launch attacks.
CNN's "New Day" asked chief Palestinian negotiator Saeb Erakat what the purpose of the tunnels were.
"I know the situation is so much complex -- I'm not saying I know the picture as a whole," he responded. But, he said, Gaza is now like a burning building. "We need to get the people out, and then we need to extinguish the fire, and then we sit down and talk."
Erakat called for Israel to pull troops out of Gaza.
Israel isn't acting in self-defense, he said. "They're the occupying power. They should be responsible for the human lives there."
Erakat said U.N. figures show "90% of those killed are women and children."
It was unclear what he was basing those figures on. The United Nations estimates that more than 70% of the Palestinians killed were civilians, including 226 youths and 117 women. More than 150 were members of armed groups, the United Nations says.
UNICEF said Monday that about two-thirds of the children killed were 12 or younger.
Israel blames Hamas for civilian deaths, saying militants encourage people to stay in their homes despite Israeli warnings that strikes are coming. Militants also use civilian facilities such as homes, schools, mosques and hospitals to launch attacks on Israeli civilians and store weapons.
Calls, hopes for peace
The Gaza crisis was discussed Monday in a joint call involving U.S. President Barack Obama. British Prime Minister David Cameron, German Chancellor Angela Merkel, French President Francois Hollande and Italian Prime Minister Matteo Renzi.
A statement from Cameron's office said the leaders agreed on "the urgent need for a lasting ceasefire in Gaza and Israel, backing the efforts of the Egyptian government to achieve this."
U.S. Secretary of State John Kerry returned to Washington after a trip to the Middle East and Paris, where he held discussions in an attempt to calm the violence. His efforts were criticized by Israeli media and Palestinian leaders.
A spokesman for U.N. Secretary-General Ban Ki-moon said Monday night that he was concerned the IDF had dropped leaflets in the northern Gaza Strip, warning thousands of residents to leave their homes and evacuate to Gaza City. If true, this would have a "devastating humanitarian impact" on Gaza residents, he said.
At a midnight meeting, the U.N. Security Council proclaimed its support for "a comprehensive peace based on the vision of a region where two democratic states, Israel and Palestine, live side by side in peace with secure and recognized borders as envisioned in Security Council resolution 1850 (2008)."
That fell short of Palestinian Ambassador Riyad Mansour's desires. He wanted the body to pass a resolution calling for the withdrawal of Israeli forces from Gaza.
"The equation is simple," Israeli Ambassador Ron Prosor said. "When it is quiet in Israel, it will be quiet in Gaza."
Obama had another phone conversation with Netanyahu on Sunday, reiterating concern about the rising Palestinian civilian deaths, Israeli deaths and the "worsening humanitarian situation in Gaza."
Israel: We're not responsible for last week's school deaths
The Israeli military said it was not responsible for anyone killed last week when an "errant Israeli mortar" hit the courtyard of a U.N. school that was shelter to many Gaza residents.
U.N. and Palestinian officials said 16 people were killed and hundreds were wounded Thursday when the school in northern Gaza was struck.
Israel Defense Forces spokesman Lt. Col. Peter Lerner said militants had fired anti-tank missiles from the immediate area of the school, and the IDF fired several mortar shells back in that direction.
"A single errant Israeli mortar landed in the courtyard in the school," Lerner said. "The footage we have shows the courtyard was empty."
"We reject the claim that people were killed by the IDF mortar on the school premises," he added. But Lerner said there could have been people who were wounded by shrapnel.
Israeli government spokesman, Mark Regev said, "The question is who is responsible, and for that we have to look at seriously and judiciously and make sure we get to the truth."
A CNN team that visited the shelter several hours after the mortar attack saw evidence that people were badly wounded at the courtyard.
The team saw blood and strewn possessions concentrated close to the edge of the courtyard along the wall of the building, the area that would have been shady around 3 p.m. when the school was hit.
The IDF released a high-altitude aerial video of the round hitting the school, but it did not have high resolution and it is impossible to tell if anybody was sitting on the courtyard edge.
CNN's Sara Sidner reported from Jerusalem, and CNN's Karl Penhaul reported from Gaza; Ashley Fantz and Ralph Ellis wrote from Atlanta; and Richard Roth reported from the United Nations. CNN's Holly Yan, Ali Younes, Josh Levs, Yousuf Basil, Salma Abdelaziz, Elise Labott, Tim Lister, Maryam Affane and Amir Tal contributed to this report.