Israel ordered people out of swathes of the main southern city in the Gaza Strip on Monday as it pressed its ground campaign deep into the south, sending desperate residents fleeing even as it dropped bombs on areas where it told them to go.

In Khan Younis, many of those taking flight on Monday were already displaced from other areas. Abu Mohammed told Reuters it was now the third time he had been forced to flee since abandoning his home in Gaza City in the north.

"Why did they eject us from our homes in Gaza (City) if they planned to kill us here?" he said.

At a home in Khan Younis that was struck overnight, flames licked the collapsed masonry and grey smoke billowed out from the rubble. A child's stuffed toy of a sheep lay in a pile of dust. Boys were picking through the wreckage. Next door, Nesrine Abdelmoty stood amid damaged furniture in the rented room where she lives with her divorced daughter and two-year-old baby.

"We were sleeping at 5 a.m. when we felt things collapse, everything went upside down," she told Reuters. "They told (people) to move from the north to Khan Younis, since the south is safer. And now, they've bombed Khan Younis. Even Khan Younis is not safe now, and even if we move to Rafah, Rafah is not safe as well. Where do they want us to go?"