Live updates: Follow the latest on Israel-Gaza
Two children were among civilians killed in a strike on a nursery sheltering displaced people in the city's Al Salah neighbourhood, the official Palestinian Wafa news agency reported.
Air strikes were also reported in the southern city of Khan Younis, as well as Deir Al Balah and Nuseirat refugee camp in central Gaza.
The latest wave of Israeli assault came a day after EU officials and member states urged Israel not to strike Rafah, with the city near the Egyptian border crammed with a million displaced Palestinians from across the enclave.
Fourteen women and children were killed in an Israeli strike on a Rafah home on Saturday, Gaza's Health Ministry said.
EU Foreign Affairs Minister Josep Borrell said attacks were creating a “very dire situation”, while German Foreign Office Minister Anna Luehrmann “warned emphatically” against an assault on the city.
“There are one million people in the south that have been displaced progressively against the Egyptian border,” said Mr Borrell.
“They [the Israelis] claimed that they were safe zones but in fact what we see is that the bombing affecting the civilian population continues."
Palestinians throughout Gaza have fled south in hope of reaching safety but have found little respite.
The journey to Rafah is arduous and lengthy, and attacks have been reported on civilians fleeing the fighting on foot.
"It was the most difficult night of my life," Huda Harb, from Gaza city, told The National of her overnight journey to the south.
"I witnessed death. They shot at us, they don’t care about children or elderly people,” she said of the Israeli military.
Ms Harb spent five days without food or water in a residential tower surrounded by the army.
It was later raided, with all the men arrested and the women and children instructed to move south, she said.
"My father is 70 years old," she added. "I told them to leave him but they refused and took him. They forced the men to take off their clothes and it was cold and raining."
She walked south with her four daughters, having been forced to leave all their belongings behind.
"There was an old woman with us and suddenly she collapsed and couldn't move. She asked me to leave her. There were dogs around us and I didn't know what could happen to her."
The group was also forced to leave seven people in wheelchairs who were unable to make the hours-long journey.
At least 27,238 people have been killed and another 66,452 wounded in Israeli attacks on Gaza since the war began on October 7, the enclave's Health Ministry said.
Gaza's fragile health sector has been devastated by the fighting, with only nine of 32 hospitals still running, at a fraction of their usual capacity, the World Health Organisation said.
US, Egyptian and Qatari officials have been working for weeks to finalise a ceasefire deal that would secure a new pause in fighting in return for the release of Israeli hostages still held in Gaza, estimated at about 132.
Domestic calls for a deal have also continued in Israel, where thousands rallied on Saturday night in Tel Aviv and other cities to push Prime Minister Benjamin Netanyahu to reach an agreement.
“It's either a deal or a death sentence,” said former Israeli army spokesman Avi Benayahu.
“We'll need to free prisoners, we'll need to have a long ceasefire,” he said. “Hamas will still be there and Israel will still be there.” Israeli newspaper Haaretz quoted him as saying.
US Secretary of State Antony Blinken will begin a fresh regional tour on Sunday aimed at securing a hostage deal and getting more humanitarian aid into Gaza amid an increase in diseases.
French Foreign Minister Stephane Sejourne is also in the region to discuss a postwar future and the current tensions between Israel and Hezbollah.
“There will be a discussion with his regional counterparts, especially Israeli and Palestinian counterparts, to see how to restart a political perspective in the region,” deputy Foreign Ministry official Christophe Lemoine said.
Israel has maintained its opposition to a permanent end to the fighting until Hamas, which killed 1,200 people in its attack on southern Israel, is “completely eradicated”.
The militant group has said a deal is not yet finalised and it needs more time to announce its position.
On Saturday, Osama Hamdan, a top Hamas official in Lebanon, said a proposal had been received but some details were missing and a final agreement had yet to be reached.