Health officials said an Israeli air strike on a house in Rafah, where more than half of Gaza's 2.3 million residents are now homeless, killed 14 people including women and children.
The Israeli military did not immediately respond to a request for comment.
Israel's Defence Minister Yoav Gallant said forces would now press on to Rafah on Gaza's southern edge.
Tens of thousands have arrived in Rafah in recent days, carrying belongings in their arms and pulling children on carts, since Israeli forces last week launched one of their biggest assaults of the war to capture nearby Khan Younis, the main southern city.
"The place turned black, I couldn't see what's in front of me. It was all dust and dirt. I was touching my surroundings, I was looking for my mobile to use the flashlight to look for my children, where are they? I found them under the rubble," said Ahmed Bassam Al-Jamal, whose son was killed.
"I cried for help and people came. I got out Yamen, the first one, he was the only one I can see, the rest were still under the rubble. They pulled out Yamen, Eileen and Sila and they pulled out their mother (all alive). We could not find Bassam, we were looking for him, but he was buried, we could not save them, I swear we couldn't," Jamal said, as he bade farewell to his dead son at the hospital.
In the central Gaza Strip city of Deir Al-Balah, the second major concentration of displaced people, medics said four people were killed in an air strike on a house earlier on Saturday.
In nearby Khan Younis, residents said the army blew up a residential district near the city centre.
The Gaza health ministry said heavy Israeli bombardment around the city's two main hospitals continued to undermine healthcare systems and endanger the lives of staff, patients, and displaced people who have taken shelter there.
On Friday, the Palestinian Red Crescent Society said four people were killed by Israeli gunfire directed against the Al-Amal Hospital.
In Gaza City, residents and militants said fighting continued against Israeli forces. Health officials said two people were killed by sniper fire. Israeli forces carried out arrests in the southern suburb of Tel Al-Hawa.
Israel launched a war on Hamas, the militant group which rules the Gaza Strip, after an October onslaught on southern Israel by Hamas militants who killed 1,200 people and took 253 people hostage into Gaza, more than 100 of whom are still captive, according to Israeli tallies.
Israeli officials say they aim to eliminate Hamas, which has vowed to repeat its October attacks, and repatriate the hostages, many of whom are women and children.
Gaza health authorities, who do not differentiate between militants and civilians in their tallies, say more than 27,000 Palestinians have been confirmed killed since the start of the war, 107 of them in the past 24 hours, with thousands more feared lost amid the ruins.
The Israeli military said its forces killed dozens of Palestinian gunmen in northern Gaza.
"During targeted raids in the northern and central Gaza Strip over the last day, IDF troops killed dozens of terrorists and destroyed numerous anti-tank missile launchers," the Israel Defense Forces said.
Hamas, Islamic Jihad, and other smaller militant groups said in a separate statement their fighters engaged in fierce battles with the army in the north and the south of the Gaza Strip.
"The more the occupation forces remain on the ground, the more we will get to them," one Palestinian militant official said.
"A martyr falls, another rises and takes the rifle, and we are ready to fight for many more months," he told Reuters.
Asked about Israel saying it killed 10,000 militants, he said, "This is for public consumption in the occupation entity. It is fiction."
CEASEFIRE PROPOSAL
Mediators are awaiting a response from Hamas to a proposal for the war's first extended ceasefire, drafted last week with Israeli and U.S. spy chiefs and communicated by Egypt and Qatar. It was unclear when Hamas leaders would visit Cairo to respond.
A brief November truce lasted just one week, when militants freed 110 women, children and foreign hostages in exchange for Palestinians held in Israeli jails.
On Friday, Hamas chief Ismail Haniyeh, who is leading negotiations with Qatar and Egypt, said he spoke to the chief of the Islamic Jihad, an ally of Hamas, and the leader of the Popular Front for the Liberation of Palestine, to discuss the ceasefire proposal.
A Hamas statement said the discussions stressed that: "Any negotiations should lead to a complete end to the aggression, the withdrawal of the occupation army outside the Gaza Strip, the lifting of the siege," as well as reconstruction, provision for Gaza's basic needs and a full exchange of captives.
However, Israel says Hamas must be eradicated before it pulls its troops out or frees detainees, and its main ally, the United States, has not publicly set any goals that call that into question.
(Reporting and writing by Nidal al-Mughrabi in Doha; additional reporting by Emily Rose in Jerusalem, Ibraheem Abu Mustafa in Gaza; Editing by Giles Elgood)
By Nidal al-Mughrabi and Ibraheem Abu Mustafa
