GAZA CITY, Gaza Strip — The U.N. chief and the U.S. Secretary of State headed to Cairo today for the highest-level attempt yet to end two weeks of Israel-Hamas fighting that has killed at least 510 Palestinians and 20 Israelis and driven tens of thousands of Gaza residents from their homes.

Despite the new cease-fire efforts by U.N. Secretary-General Ban Ki-moon and U.S. Secretary of State John Kerry, Israeli aircraft continued to strike homes in Gaza while Hamas fired more rockets and tried to infiltrate into Israel.

In one Israeli strike, 25 people were buried under the rubble of a home in the southern town of Khan Younis, including 24 from the same family.

“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.”

Israeli tank shells today struck a hospital in central Gaza, a health official and a doctor at the facility said. The health official said the shells killed at least four people and wounded 60, including 30 medical staff.-

The shells hit the Al Aqsa hospital in the town of Deir el-Balah.

Meanwhile, Hamas militants 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.

Despite the rising death toll, there was no sign of a letup in the violence.

Israeli Defense Minister Moshe Yaalon said today he is prepared to continue the offensive “as long as necessary” to halt rocket fire and other attacks from Gaza on Israelis.

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 is also pushing for an unconditional cease-fire.

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.

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.

Israel launched a ground offensive 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.

Early today, an 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, said Palestinian health official Ashraf al-Kidra.

The attacks came a day after the first major ground battle of the offensive, in the Shijaiyah neighborhood of Gaza City.

At least 65 Palestinians and 13 Israeli soldiers were killed in Shijaiyah, while thousands of terrified Palestinian civilians fled the devastated area, which Israel says is a major source for rocket fire against its civilians.

Large sections of Shijaiyah were pulverized by a barrage of Israeli tank and artillery bombardments and repeated Israeli air strikes that buffeted the densely populated neighborhood for most of Sunday.