Intense fighting was under way simultaneously in the north and south of the enclave, a day after the United Nations demanded an immediate humanitarian ceasefire.
US President Joe Biden said Israel's indiscriminate bombing of civilians was costing international support.
Warplanes again bombed the length of Gaza and aid officials said the arrival of rainy winter weather worsened the conditions for hundreds of thousands of families sleeping rough in makeshift tents. The vast majority of Gaza's 2.3 million people have already been made homeless.
Israel reported ten of its soldiers killed in the past 24 hours, including a full colonel commanding a forward base and a lieutenant-colonel commanding a regiment. It was the worst one-day loss since 15 were killed on October 31.
Most of the deaths came in the Shejaiya district of Gaza City in the north, where troops were ambushed trying to rescue another group of soldiers who had attacked fighters in a building, the military said.
Hamas said the incident showed that Israeli forces could never subdue Gaza. "The longer you stay there, the greater the bill of your deaths and losses will be, and you will emerge from it carrying the tail of disappointment and loss, God willing."
In the south, Israeli forces storming Khan Younis advanced in recent days to city centre. Residents said there was heavy fighting there but no further attempts to advance in the last 24 hours.
“The Israeli tanks have not moved further from the centre of the city. They are facing fierce resistance and we hear the exchanges of fire, explosions too,” Abu Abdallah, a father of five who lives 2 km away, told Reuters.
The Israelis had brought bulldozers and were destroying the road near the Khan Younis home of the Hamas leader in Gaza, Yahya Al-Sinwar, Abu Abdallah said.
International agencies say the limited aid reaching Gaza is being distributed only in parts of Rafah near the Egyptian border. Even there, the situation has become far more extreme this week.
Gemma Connell, based in Rafah as Gaza team leader for the UN humanitarian office OCHA, told Reuters in a message. Heavy rains and winds overnight are awful for all of these people in makeshift shelters.
Israel says it has been encouraging increased aid to Gaza through Egypt's border, and is announcing daily four-hour pauses in operations near Rafah to help civilians reach it. The UN says cumbersome inspections and insecurity have slowed aid to a trickle.
The UN General Assembly vote demanding a ceasefire has no legal force but was the strongest sign yet of eroding international support for Israel's actions. Three-quarters of the 193 member states voted in favour and only eight countries joined the United States and Israel in voting against.
Before
the vote, Biden said Israel still has support from "most of the
world" for its fight against Hamas.
"But they're starting to lose that support by indiscriminate bombing that takes place," he told a campaign donor event.
In the most public sign of division between the US and Israeli leaders so far, Biden said Prime Minister Benjamin Netanyahu needed to change his hardliner government, and that ultimately Israel can't say no to an independent Palestinian state, opposed by far-right members of the Israeli cabinet.
