Medics said two strikes targeted the Karama School in Tuffah, a suburb of Gaza City, killing 15 on Wednesday. Later in the day, an Israeli strike near a restaurant and market in the city killed at least 33 people, including women and children, medics said.
There was no immediate Israeli comment.
Reuters footage of the scene near the market showed wounded men being rushed away on the back of pickups and carts. Ambulances sped down shattered streets and a woman in tears carried a baby away from the scene, with two young children beside her.
"The blood was like a lake, oh my baby, pools of blood," she screamed.
An image posted on social media showed what appeared to be a family of three - mother, father and son - lying dead on the street in pools of blood. The young boy was carrying a pink backpack. Reuters could not immediately verify the image that was purportedly from the scene near the restaurant.
Two Israeli air strikes on another school, housing displaced people in Bureij camp in central Gaza, killed at least 33 people, including women and children, on Tuesday, local health authorities said. The Israeli military said it struck "terrorists" operating from a command centre in the compound.
The strike smashed classrooms, destroyed furniture and left a large crater in the school campus. On Wednesday, survivors sifted through rubble to look for some of their belongings.
In Rafah in the southern Gaza Strip, near the border with Egypt, residents and Hamas sources said Israeli forces, who have taken control of the city, continued to blow up and demolish houses and buildings.
Al-Qassam Brigades, the military wing of the Palestinian militant group Hamas, said on Wednesday their fighters had detonated a pre-planted minefield targeting an Israeli armoured force east of Khan Younis in the south. They said they inflicted casualties, followed by mortar shelling of the area.
Israel resumed its offensive in March after the collapse of a US-backed ceasefire that had halted fighting for two months. It has since imposed an aid blockade, drawing warnings from the UN that the 2.3 million population faces imminent famine.
Israeli troops have already taken over an area amounting to around a third of Gaza, displacing the population and building watchtowers and surveillance posts on cleared ground the military has described as security zones.
Israeli Prime Minister Benjamin Netanyahu has said he will expand the offensive against Hamas after his security cabinet approved plans that may include seizing the entire Gaza Strip and controlling aid.
But an Israeli defence official said on Monday the operation would not be launched before US President Donald Trump concludes his visit next week to the Middle East, and there was a "window of opportunity" for a ceasefire and hostage release deal during Trump's visit.
A senior Hamas official, Bassem Naim, said on Wednesday the group would not agree to any interim truce in return for a resumption of aid for a few days, and insisted on a full ceasefire deal to end the war.
Naim said Hamas would not accept "desperate attempts before Trump's visit, through the crime of starvation, the continuation of genocide, and the threat of expanding military action to achieve a partial agreement that returns some (Israeli) prisoners in exchange for a few days of food and drink".
The war began on October 7, 2023, when Hamas killed 1200 people and took 251 hostage, according to Israeli tallies.
Israel's campaign has killed more than 52,000 Palestinians, mostly civilians, according to Hamas-run health authorities, and reduced much of Gaza to ruins.
The Hamas-run Gaza government's media office said two local journalists, Nour Abdu and Yehya Sbeih, were killed in Wednesday's attacks, raising the number of Palestinian journalists killed by Israeli fire since the war began to 214.
