An Israel Defence Forces official said ground troops were moving deeper into the enclave's main city and that the number of soldiers would rise in coming days to confront up to 3000 Hamas combatants the IDF believes are still in the city.
"Gaza is burning," Defence Minister Israel Katz posted on X.
"The IDF strikes with an iron fist at the terrorist infrastructure and IDF soldiers are fighting bravely to create the conditions for the release of the hostages and the defeat of Hamas."
In launching the assault, Israel's government defied European leaders threatening sanctions and warnings from even some of Israel's own military commanders that it could be a costly mistake.
US President Donald Trump told reporters at the White House that Hamas would have "hell to pay" if it used hostages as human shields during the assault.
Israeli Prime Minister Benjamin Netanyahu said Trump had invited him to the White House in two weeks, after both men have addressed an annual gathering of world leaders at the United Nations General Assembly.
In the latest expression of international alarm, a United Nations Commission of Inquiry concluded that Israel had committed genocide in the Gaza Strip.
Israel called the assessment "scandalous" and "fake".
United Nations Secretary-General Antonio Guterres said that what is happening in the enclave was horrendous and that the war in the Palestinian territory was morally, politically and legally intolerable.
Palestinian local health authorities said an Israeli strike had hit a vehicle carrying displaced people fleeing south near the coastal road in Gaza City.
The latest deaths take Tuesday's toll to at least 75, most of them in Gaza City.
The Israeli military did not immediately comment on the strike.
Where a missile had destroyed two multi-storey residential buildings during the night, people clambered over an immense mound of dislocated concrete to pry out victims, footage obtained by Reuters showed.
A woman cried as a small child's body was pulled from the wreckage, hastily wrapped in a green blanket and carried away.
Abu Mohammed Hamed said several of his relatives had been wounded or killed, including a cousin whose body was trapped by a concrete block: "We don't know how to take her out. We have been working on it since 3am."
Israel renewed calls on civilians to leave, and columns of Palestinians streamed towards the south and west in donkey carts, rickshaws, heavily laden vehicles or on foot.
"They are destroying residential towers, the pillars of the city, mosques, schools and roads," Abu Tamer, a 70-year-old man making the journey south with his family, told Reuters in a text message.
"They are wiping out our memories."
Hours before the escalation, US Secretary of State Marco Rubio said in Jerusalem that while the United States wished for a diplomatic end to the war, "we have to be prepared for the possibility that's not going to happen".
In Brussels, a spokesperson for the European Union executive said it would agree on Wednesday to impose new sanctions on Israel, including suspending certain trade provisions.
Netanyahu told a press conference on Tuesday that if there was one lesson learned from the Gaza Strip war it was that Israel needs to create an "independent weapons industry" that can "withstand international constraints".
Some Israeli military commanders have expressed concern that the Gaza City assault could endanger remaining hostages held by Hamas or be a "death trap" for troops.
Chief of Staff Eyal Zamir, at a meeting Netanyahu convened late on Sunday with security chiefs, urged the prime minister to pursue a ceasefire deal, according to three Israeli officials, two of whom were in the meeting and one of whom was briefed on its details.
Hamas attacked Israel in October 2023, killing about 1200 people and taking 251 hostages, Israeli tallies show.
Israel's military assault against Hamas has killed more than 64,000 Palestinians, Gaza's health ministry says.
