Ban, who released the statements from Doha, will also travel to Kuwait City, Cairo, Jerusalem, Ramallah and Amman. He is to meet Egyptian President Abdel Fattah El Sisi in Cairo on Monday to discuss proposals to arrange a truce in the conflict.

"Israel must exercise maximum restraint and do far more to protect civilians," Ban said, adding that it also "must respect the humanitarian law."

Among the calls from the international community to curtail its campaign in Gaza, was United Nations Secretary-General Ban Ki-moon urging Israel on Sunday to "exercise maximum restraint" and spare the lives of civilians. He also condemned the "atrocious action" of Israel in besieged Shujaeya.

An Israeli captive in Hamas' hands would force Prime Minister Benjamin Netanyahu to confront a tough choice on whether to escalate Israel's operation even as international pressure mounts for a halt, or to pursue a cease-fire on terms that would include that soldier’s release — and, inevitably, involve more concessions to Hamas than he’d prefer to make.

Hamas is well aware of the effect holding Israelis captive has on the national psyche of their adversary — after holding Sgt. Gilad Shalit for more than five years, the movement forced Israel to release more than 1,000 Palestinan prisoners in exchange for his release. (A number of those released were rounded up by Israel in the crackdown that followed the abduction of three teenage Israelis in the West Bank, who were later found dead.)

Isreal's military confirmed that 13 of its soldiers were killed in overnight fighting, bringing the total death toll of IDF soldiers to 18.

Palestinians in Gaza ended the most devastating day of Israel’s bombardment on a celebratory note, after Hamas’ military wing announced it had captured an Israeli soldier. A masked spokesman for the Al-Qassam Brigades gave the name and military ID number of the alleged captive, prompting cheers in Gaza and in Palestinian communities beyond — but Israel has yet to confirm or deny the claim. The report came after the eastern Gaza district of Shujayea was hit hard by Israeli tank shelling, leaving at least 60 dead and injuring at least 250 others, in the 13th day of the operation that has killed 440 Palestinians.

Devastation in Shujayea

Both the Israelis and Palestinians had, early on Sunday, agreed to observe a two-hour humanitarian cease-fire in Shujayea to allow the evacuation of the wounded, but the pause lasted less than an hour.

Israel's military said its forces were shot at shortly after the start of the two-hour truce, which was facilitated by the Red Cross. Israel resumed combat operations shortly after the reported action. The Palestinian Hamas movement did not respond to the accusation that it had resumed fire. Instead, Palestinian Authority President Mahmoud Abbas accused Israel of carrying out a massacre and declared three days of mourning.

Amid the intensified shelling, hundreds of desperate civilians scrambled to Gaza City. People traveled on foot carrying children and plastic bags filled with their belongings.

In Shujayea, dozens of bodies were brought to hospitals, and more were expected to arrive as ambulances tried to access the besieged neighborhoods.

A Shujayea resident who reached a hospital told Al Jazeera: "It is a massacre taking place in Shujayea. It is a massacre with the full sense of the word, committed by Israel against innocent civilians, there are no armed men among us, the streets of Shujayea are packed with dead bodies."

Ibtessam Batniji, 29, walked the streets of Shujayea, looking in vain for a taxi with her children.

"Children are scared. We wanted to leave earlier, but we did not dare to go out in the dark," she told Al Jazeera. "It was like a ghost town, the smell of death and the sound of shooting and shelling everywhere."

Israel says it is targeting military installations of Hamas and other armed groups. But the vast majority of those who have been killed and injured are Palestinian civilians, many of them children.

Waleed, a resident of Gaza's eastern al-Shaff area, told Al Jazeera that he was terrified and stuck with his family of 18 members in a single room and had nowhere to go while Israeli shelling continued through the night.

"We can hear shells and rockets fall on our streets and homes. They're falling everywhere," he said.

"We have no electricity, everything has been cut off. The Red Cross can't reach the area — it's too dangerous. People are stuck at home. All we hear is shelling."

Mads Gilbert, a Norwegian doctor working at Gaza's al-Shifa hospital, told Al Jazeera that most of the casualties brought there were civilians who suffered shrapnel injuries and amputations.

"It's very disturbing to see the large number of civilians, particularly the children.”

The Israeli bombardment has heightened a refugee crisis in Gaza, with the U.N. reporting that more than 60,000 people are in need of shelter.

Meanwhile, politicians in the U.S. and Israel defended the country’s actions in Gaza.

Kerry also said Sunday that Israel “has every right in the world to defend itself” from attacks by Hamas, and that he supported a cease-fire, but blamed Hamas for the continued violence.

"They've been offered a cease-fire, and they've refused to take the cease-fire," he said.

Netanyahu also blamed Hamas for most of the violence in Gaza, saying the group was using civilians as human shields, which Hamas denies.

Hamas rejected an Egyptian-brokered truce, saying any deal must include an end to a blockade of the coastal area and a recommitment to a cease-fire reached after an eight-day war in Gaza in 2012.

President Obama and Netanyahu spoke on the phone Sunday, their second call in three days to discuss the situation in Gaza. Obama reiterated the United States’ condemnation of attacks by Hamas against Israel, and reaffirmed Israel’s right to defend itself, but raised concern about the growing number of casualties, including the increasing Palestinian civilian deaths in Gaza and the loss of Israeli soldiers.

Obama told Netanyahu that Kerry will soon travel to Cairo to seek an immediate cessation of hostilities based on a return to the November 2012 cease-fire agreement.

Wire services, with reporting by Stefanie Dekker in Gaza