Israel said the aims of its war against the Hamas movement that runs Gaza were unchanged and that efforts were being made to bring about the release of more than 100 Israeli hostages.
Military spokesman Rear Admiral Daniel Hagari said 21 soldiers were killed when two buildings they had mined for demolition exploded after militants fired at a nearby tank. Three soldiers were reported killed in a separate attack.
"Yesterday we experienced one of our most difficult days since the war erupted," Prime Minister Benjamin Netanyahu said. "In the name of our heroes, for the sake of our lives, we will not stop fighting until absolute victory."
Asked about media reports that a ceasefire deal was being discussed, after Qatar said mediation efforts were ongoing, Israeli government spokesperson Eylon Levy said the war's goals were unchanged.
"The destruction of Hamas' governing and military capabilities in the Gaza Strip and the return of all the hostages," he said. "There will be no ceasefire that leaves the hostages in Gaza and Hamas in power."
Levy declined to elaborate on efforts to free the hostages, who were taken to Gaza following the October 07 rampage in which Hamas and other militants killed some 1,200 Israelis - the trigger for the war. Levy said lives were in the balance.
The soldiers' deaths came the day the Israeli Defence Forces (IDF) launched their biggest operation in a month, to seize remaining parts of Khan Younis, Gaza's main southern city, which is sheltering hundreds of thousands of displaced Palestinians.
"Over the past day, IDF troops carried out an extensive operation during which they encircled Khan Younis," the military said, adding that they had "eliminated" dozens of fighters.
Israeli tanks, advancing west towards the Mediterranean, shut the road out towards the coast on Tuesday, blocking the escape route for civilians trying to reach Rafah, the last town on Gaza's southern edge - now crammed with more than half the enclave's 2.3 million people.
At least 195 Palestinians were killed in the space of 24 hours, raising the documented toll to 25,490, according to Palestinian health officials, who say thousands more dead are feared lost in the rubble.
