Meanwhile, U.N. chief Ban Ki-moon and U.S. Secretary of State John Kerry headed to Cairo to try to renew cease-fire efforts aimed at ending the Israel-Hamas fighting that has killed at least 530 Palestinians and 20 Israelis and displaced tens of thousands of Gazans in the past two weeks.
Despite the new diplomatic push, Israel continued to attack targets in the densely populated coastal strip from the air and from tanks, while Hamas fired more rockets and tried to infiltrate into Israel.
A dozen shells hit the Al Aqsa hospital in the town of Deir el-Balah on Monday, Palestinian health official Ashraf al-Kidra said. He said four people were killed and 60 wounded when the shells landed in the administration building, the intensive care unit and the surgery department.
Live footage on Hamas' Al Aqsa TV station showed wounded being moved on gurneys into the emergency department.
A doctor at the hospital, Fayez Zidane, told the station that shells hit the third and fourth floor as well as the reception area.
The Israeli military said it was looking into the report.
In one of several airstrikes, 25 people were buried under the rubble of a home in the southern town of Khan Younis, including 24 from the same family. Rescue workers pulled the bodies from the wreckage Monday.
"Twenty-five people!" said family member Sabri Abu Jamea. "Doesn't this indicate that Israel is ruthless? Are we the liars? The evidence is here in the morgue refrigerators. The evidence is in the refrigerators."
Another Israeli airstrike hit the home of the Siyam family in southern Gaza, near the town of Rafah, said the Palestinian Center for Human Rights. The strike killed 10 people, including four young children and a 9-month-old baby girl, al-Kidra said.
Hamas militants, meanwhile, tried to sneak into Israel through two tunnels, the latest in a series of such attempts. The Israeli military said 10 infiltrators were killed after being detected and targeted by Israeli aircraft.
Hamas also fired 50 more rockets at Israel, including two at Tel Aviv, causing no injuries or damage. Since the start of the Israeli operation, Hamas has fired almost 2,000 rockets at Israel.
Israeli Defense Minister Moshe Yaalon said the Gaza military operation would have no time limit.
"If needed we will recruit more reservists in order to continue the operation as long as necessary until the completion of the task and the return of the quiet in the whole of Israel especially from the threat of the Gaza Strip," Yaalon told a parliamentary committee.
Israel accepted an Egyptian call for an unconditional cease-fire last week, but resumed its offensive after Hamas rejected the proposal.
Hamas says that before halting fire, it wants guarantees that Israel and Egypt will significantly ease a seven-year border blockade of Gaza.
"The resistance (Hamas) will not respond to any pressure," Hamas spokesman Sami Abu Zuhri said in a text message, in a reference to the renewed cease-fire efforts.
Kerry left Washington early Monday for Cairo, where he will join diplomatic efforts to resume a truce that had been agreed to in November 2012.
Hamas remains deeply suspicious of the motives of the Egyptian government, which has banned the Muslim Brotherhood, a region-wide to which Hamas also belongs.
Israel invaded Gaza late last week, preceded by a 10-day air campaign. Air and artillery strikes have targeted Gaza's border areas in an attempt to destroy tunnels and rocket launchers.
Sunday marked the single deadliest day in Gaza since the conflict erupted on July 8, with more than 100 Palestinians killed, according to Palestinian health officials. Most died in the first major ground battle of the conflict, in Gaza City's Shijaiyah neighborhood, which Israel says is a major source for rocket fire against its civilians.
In response to the escalation, the U.N. Security Council expressed "serious concern" about the rising civilian death toll and demanded an immediate end to the fighting.
On Sunday afternoon, rescue workers making a last sweep through Shijaiyah had heard the voice of a woman under the rubble, pleading for help.
The team left because it deemed the situation too dangerous, but returned later Sunday with a bulldozer to rescue the three people trapped underneath.
Seven-year-old Bissam Dhaher, her face bruised and bandaged, was recovering Monday at Gaza City's Shifa Hospital. Relatives watched over her as the girl slept. Her uncle remained hospitalized, while an aunt - the one who had called out for help - was released, relatives said.
On Sunday evening, Hamas spokesman Mushir al-Masri in Gaza claimed his group had captured an Israeli soldier. An announcement on Gaza TV of the soldier's capture set off celebration in the streets of West Bank.
But there was no official confirmation or denial of the claim in Israel.
For Israelis, a captured soldier would be a nightmare scenario. Hamas-allied militants seized an Israeli soldier in a cross-border raid in 2006 and held him captive in Gaza until Israel traded more than 1,000 Palestinian prisoners, some of whom were involved in grisly killings, for his return in 2011.
Enav reported from Jerusalem.