On Saturday morning, Israeli war planes attacked areas close to the Khan Younis Nasser Hospital six times, according to medics and witnesses.
The hospital is filled with thousands of displaced and hundreds of wounded, including many of those who had been evacuated from north Gaza hospitals.
"A night of horror," said Samira, a mother of four. "It was one of the worst night we spent in Khan Younis in the past six weeks since we arrived here," she said. "We are too afraid they will enter Khan Younis."
The Israeli military said that in the last 24 hours combined attacks by its ground, air and naval forces had hit 400 militant targets and killed an unspecified number of Hamas fighters.
The conflict broke out on Oct. 7 when Hamas militants crossed into southern Israel and killed 1,200 people, mostly civilians, in a rampage against kibbutzim and other communities. More than 200 hostages were taken back into Gaza.
Israel responded with a bombing campaign and a ground offensive which has destroyed large areas of Gaza in what has become the bloodiest episode of the wider Israel-Palestinian conflict.
Leaflets dropped by Israel on eastern areas of Khan Younis ordered residents of four towns to evacuate - not to other areas in Khan Younis as in the past, but further south to Rafah.
Residents took to the road with belongings heaped up in carts, searching for shelter further west.
In Rafah, residents carried several small children, streaked with blood and covered in dust, out of a house that had been struck. Mohammed Abu-Elneen, whose father owns the house, said it was sheltering people displaced from elsewhere.
Islamic Jihad's armed wing Al-Quds Brigades said its fighters had fired mortar bombs at Israeli forces massed in Kissufim in the southern Gaza Strip east of Khan Younis and Deir Al-Balah.
The Israeli military said it had killed many fighters in northern Gaza, including in a gunbattle at a mosque used by Islamic Jihad militants as a command post.
In southern Israel, rocket sirens sounded early on Saturday in communities near the border with Gaza, but there were no reports of serious damage or casualties.
Reuters could not confirm the battlefield accounts.