The heavy clashes came as a White House official was due in the region for talks aimed at securing more hostage releases, and as US media reported a new Israeli proposal for a deal that would involve a two-month pause in fighting.
Twenty-four soldiers were killed on Monday, with army spokesman Daniel Hagari saying 21 of them were reservists slain when rocket-propelled grenade fire hit a tank and two buildings they were trying to blow up.
Prime Minister Benjamin Netanyahu said the army had launched an investigation into the "disaster," More than 200 soldiers have been killed since Israel launched its ground operations in Gaza.
"We must learn the necessary lessons and do everything to preserve the lives of our warriors," Netanyahu said.
An analyst said the mounting Israeli toll would heap pressure on the government.
"Everybody is mourning the soldiers this morning and I think people will demand clear answers about the purpose and the goal of this operation in Gaza," said Israela Oron of the Ben-Gurion University of the Negev.
The army said Tuesday its forces had "encircled" Khan Yunis, and "deepened" their operations in the densely populated city after killing dozens of militants over the past 24 hours.
Witnesses said huge explosions shook Khan Yunis, southern Gaza's main city, as well as Deir al-Balah in north Gaza and Rafah in the south.
Medical charity Doctors Without Borders (MSF) said its staff at the Nasser Hospital in Khan Yunis felt the "ground shaking."
"There is a sense of panic among staff, patients and displaced people sheltering inside the building," it said on social media platform X.
The Palestinian Red Crescent said Israeli forces had hit its headquarters in Khan Yunis "resulting in injuries among internally displaced individuals who sought safety on our premises."
Hostage talks
UN agencies and aid groups have sounded the alarm about the growing threat of disease and famine in Gaza, where 1.7 million people are estimated to have been displaced from their homes.
Abu Iyad, his belongings piled on a donkey-drawn cart, said he was moving for the seventh time, fleeing Khan Yunis for Rafah on the Egyptian border, where hundreds of thousands of displaced Palestinians have sought shelter, many in makeshift tents.
"I'm heading to the unknown," he told AFP. "They told us to go to Rafah—where to go in Rafah? Is there any space left?"
The Gaza war broke out with Hamas's unprecedented October 7 attacks, which resulted in the deaths of about 1,140 people in Israel, mostly civilians, according to an AFP tally based on Israeli official figures.
In response, Israel has carried out a relentless offensive that has killed at least 25,490 people in Gaza, around 70 percent of them women, children and adolescents, according to the health ministry in the Hamas-run territory.
The Hamas attack also saw about 250 hostages seized, and Israel says around 132 remain in Gaza. That number includes the bodies of at least 28 dead hostages, according to an AFP tally based on Israeli figures.
A week-long truce in November saw 105 hostages released, the Israelis among them in exchange for Palestinian prisoners held in Israeli jails.
Relatives of those still held captive stormed a parliamentary committee meeting on Monday demanding urgent action.
"You sit here while our children are dying over there," yelled Gilad Korngold, father of hostage Tal Shoham, an AFP correspondent reported.
Two-state solution
US news outlet Axios reported on Monday night that Israel had proposed to Hamas, via Qatari and Egyptian mediators, a new deal to free all the hostages.
The report, citing unnamed Israeli officials, said the proposed deal would be carried out in multiple stages, and would also involve the release of an undetermined number of Palestinian prisoners.
The plan was expected to take about two months to complete.
The proposal does not include promises to end the war, but it would involve Israeli troops reducing their presence in major cities in Gaza and gradually allowing residents to return to the territory's devastated north, Axios said.
News of the proposal comes as US media said the White House's coordinator for the Middle East, Brett McGurk, was expected in Egypt and Qatar for meetings aimed at securing a new hostage exchange deal.
State Department spokesman Vedant Patel, however, said Washington still believed "a two-state solution, a creation of a Palestinian state, is the only path that gets us out of this endless cycle of violence."
Netanyahu has steadfastly rejected calls for the creation of a Palestinian state, saying Israel must maintain "security control over all the territory west of the Jordan" River, an area that includes all of the Palestinian territories.
US, UK hit Yemen's Houthis
EU foreign ministers pressed Israel to change its mind at meetings in Brussels on Monday with the top diplomats from the two warring parties and key Arab states.
"The two-state solution is the only solution, and even those who don't want to know about it have not yet come up with any other alternative," said German Foreign Minister Annalena Baerbock.
At the gathering, Israeli Foreign Minister Israel Katz ignored questions from journalists over a future two-state solution and said his country was focused on returning the hostages and ensuring its security.
Jordanian Foreign Minister Ayman Safadi, who was also in attendance, said Israel's rejection of "the two-state solution is dooming the future of the region to more conflicts."
The Gaza war spurred fears of a wider escalation, with a surge in violence involving Iran-backed Hamas allies across the region.
Lebanon's Shiite movement Hezbollah said Tuesday it targeted an Israeli command centre with a large number of missiles in response to Israeli "assassinations" and attacks on civilians.
The United States and Britain launched a new wave of air strikes against Yemen's Iran-backed Houthi rebels on Tuesday over their attacks on Red Sea shipping.
In response, the Houthis warned that "these attacks will not go unanswered and unpunished."
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