Under US pressure to prevent further mass casualties, Israel says it is being more precise as it widens its offensive into southern Gaza after obliterating much of the north.
But Palestinians say there are no areas where they feel safe, and many fear that if they leave their homes they will never be allowed to return.
Aerial bombardment and the ground offensive have already driven three quarters of the territory's 2.3 million people from their homes, and new orders to evacuate areas around Khan Younis are squeezing people into ever-smaller areas of the already tiny coastal strip.
At the Nasser Hospital in Khan Younis, ambulances brought dozens of wounded people in. At one point, a car pulled up and a man emerged carrying a young boy in a bloody shirt, whose hand had been blown off.
"What's happening here is unimaginable," said Hamza al-Bursh, who lives in the neighborhood of Maan, one of several in and around the city where Israel has ordered civilians to leave. "They strike indiscriminately."
Palestinians say there is nowhere they feel safe and many fear they will never be allowed to return. (AP PHOTO)
Residents said troops had advanced following heavy airstrikes to Bani Suheila, a town just east of Khan Younis. Halima Abdel-Rahman, who fled to the town earlier in the war from her home in the north, said they could hear explosions through the night.
"They are very close," she said. "It's the same scenario we saw in the north."
Satellite photos from Sunday showed around 150 Israeli tanks, armored personnel carriers and other vehicles just under 6km north of the heart of the city.
Israel ordered the full-scale evacuation of northern Gaza in the early days of the war and has barred people who left from returning.
In the south, it has ordered people out of nearly two dozen neighbourhoods in and around Khan Younis. That further reduced the area where civilians can seek refuge in central and southern Gaza by more than a quarter.Â
"Nowhere is safe in Gaza, and there is nowhere left to go," Lynn Hastings, the UN humanitarian coordinator for the Palestinian territories, said Monday.
"The conditions required to deliver aid to the people of Gaza do not exist. If possible, an even more hellish scenario is about to unfold."
Israel says it must dismantle Hamas' extensive military infrastructure and remove it from power in order to prevent a repeat of the October 7 attack that ignited the war.
The surprise assault through the border fence saw Hamas and other Palestinian militants kill about 1200 people, mostly civilians, and capture some 240 men, women and children.
The military says it makes every effort to spare civilians and accuses Hamas of using them as human shields as the militants fight in dense residential areas, where they have labyrinths of tunnels, bunkers, rocket launchers and sniper nests.
Hamas is deeply rooted in Palestinian society, and its determination to end decades of open-ended Israeli military rule over millions of Palestinians is shared by the vast majority, even those opposed to its ideology and its attacks on Israeli civilians.
That will complicate any effort to eliminate Hamas without causing massive casualties and further displacement.
Even after weeks of unrelenting bombardment, Hamas' top leader in Gaza, Yehya Sinwar, was able to conduct complex ceasefire negotiations and orchestrate the release of more than 100 Israeli and foreign hostages in exchange for 240 Palestinian prisoners last week.
Palestinian militants have also kept up their rocket fire into Israel, both before and after the truce.