Ten people in a house sheltering two displaced families in Rafah were among 135 people killed in Israeli strikes over the past 24 hours, Hamas-run health ministry officials said.
The southern Gaza city's population has swollen to well over a million people as displaced people from other parts of Gaza seek safety there.
The Israel Defense Forces (IDF) said it was looking into the reports.
Rockets were also fired from Gaza into southern Israel.
Rafah resident Samir Qeshta told AFP his home had been "completely destroyed" in Israeli bombardment while he and his wife had been out.
"This house sheltered me and my children... We are peaceful people, they struck us without prior warning," he said.
Nimma al-Akhras was at home when the bombardment began.
"The strike was unimaginable," she says. "We started screaming and I couldn't move until someone carried me and put me on a cart.
"What did we do wrong? We were just sitting. It's not safe in our homes nor outside. Where can we possibly go?"
The IDF held a short pause in military activity in the city "for humanitarian purposes" following earlier strikes.
Israel says it is targeting Hamas members and their infrastructure and tries to minimise civilian casualties.
In a post on Telegram, health ministry spokesman Ashraf al-Qudra said that infrastructure and medical services in Rafah could not handle the needs of an estimated 1.3 million displacepeople.
"Rafah is reaching a breaking point because of the influx of hundreds of thousands of displaced Palestinians and their families," he said.
Doctors in the city;s Nasser hospital said they were struggling to provide care in a "collapsed" healthcare system.
"Most of the medical supplies in the ICU are missing," Dr Mohammad al-Qidra told Reuters. "We don't have empty beds, no treatments. Most of the medicines inside the emergency room are not enough for patients. We are trying to find alternatives."
Many displaced people are also using the hospital wards for shelter.
The World Health Organisation says fewer than half of Gaza's hospitals are functioning and those only partly. Very few ambulances were operational across the Gaza Strip, the Hamas-run health ministry added.
In the central Gaza Strip, residents reported intense gun battles, tank shelling and Israeli air strikes in the Bureij, Nuseirat and Maghazi refugee camps - dense urban areas.
The Israeli military said it had hit several targets there and killed numerous fighters.
The IDF also said it had killed Hamas fighters in Khan Younis, while Hamas said it had fired at an IDF helicopter near the city.
The BBC cannot verify the battlefield claims.
A total of 23,843 Palestinians, mostly civilians, have now been killed in Israel's military campaign against Hamas in Gaza, the Hamas-run health ministry says.
Israel launched its campaign after hundreds of Hamas gunmen infiltrated southern Israeli communities from Gaza, killing about 1,300 people and taking about 240 others hostage.