Throughout Monday, Israeli jets, tanks and artillery constantly pounded the densely-populated coastal strip, killing 28 members of a single family at the southern end.
At Al-Aqsa hospital in the central Gaza Strip, four people were killed and 70 wounded when an Israeli tank shell slammed into the third floor, housing operating theaters and an intensive care unit, the Health Ministry said.
The Israeli military, which has accused Hamas militants of firing rockets from the grounds of Gaza hospitals and seeking refuge there, had no immediate comment.
Non-stop attacks lifted the Palestinian death toll to 518, including almost 100 children, since fighting started on July 8, Gaza health officials said. Israel says 18 of its soldiers have also died along with two civilians.
Early Monday morning, residents of the Gaza Strip, mostly house-bound and fearful after 13 days of Israeli bombardment, lit fireworks and chanted "God is great!" after Hamas said it had captured an Israeli soldier.
Abu Ubaida, the masked and camouflaged spokesman of the Palestinian Islamist militant group's armed wing, announced that a soldier named as Shaul Alon was seized in heavy fighting on the Gaza border on Sunday.
He displayed Alon's photo ID and serial number but showed no image of him in captivity.
Israel's envoy to the United Nations denied the claim but its army has neither confirmed nor denied the report and a spokesman said on Monday: "We still cannot rule it out."
The report buoyed weary Gazans' flagging morale. If confirmed, it would fulfill long-standing promises by Hamas to grab troops in hopes of trading them for Palestinian prisoners, raising its popularity.
"Hundreds of martyrs have fallen and we're under attack 24-hours a day... but today is like a holiday and we feel joy that a soldier is in our hands and we hope more will follow," said vegetable seller Musa Abu Attiyeh, pausing as an Israeli rocket whizzed past and crashed nearby, shaking his shop.
"Abu Ubaida's words are bullets, stronger than bullets. He doesn't lie, ever," the shopkeeper said.
"Now it's the Jews' turn to feel the pressure and worry, and we will see our sons from the jails celebrating at home soon, God willing."
In Israel, the prison service said that Palestinian prisoners in 3 prisons in the south were celebrating the news of the alleged capture, and that as a result, they took away TV and yard privileges.
Ben Hartman contributed to this report.