The Jabalia refugee camp in the north of the Hamas-run enclave was among the sites hit.
A Gazan health ministry spokesperson said several people were killed by an Israeli air strike there.
Footage obtained by Reuters of the aftermath shows children covered in grey dust amid crumbled cement and rubble from collapsed buildings.
These children are crying out in search of their father. One of them says he is dead.
Civilians in the besieged territory have been seeking shelter in an ever-shrinking area of the south.
The renewed warfare comes after a seven-day pause in fighting between Israeli forces and Hamas militants ended on Friday.
Residents say bombardment from war planes and artillery has concentrated on the cities of Khan Younis and Rafah.
They add that hospitals are struggling to cope.
The following graphic images from the the Nasser Hospital in Khan Younis show bloodied casualties, including children, being rushed to the medical complex for treatment.
People could be seen crying next to casualties laid out on the hospital’s floor.
This man says he was outside a school when a rocket hit a house nearby. He brought a young boy to the hospital, but he says he died in his arms.
There was no immediate comment from Israel on the reported actions.
The violence took place despite calls from the United States - Israel's closest ally - for Israel to avoid further harm to Palestinian civilians.
Gaza's Hamas-run health ministry said more than 15,520 have been killed in nearly two months of warfare.
Israel's military response was sparked by a Hamas cross-border raid on southern Israel on October 7 in which 1,200 Israelis were killed and more than 200 taken hostage.
Israel says it is acting to annihilate Hamas, saying it poses a mortal threat to the Jewish state's very existence.
The initial Hamas attack and the ensuing war amount to the bloodiest episode in the decades-old wider Israel-Palestinian conflict.