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STORY: Palestinians from Gaza City are once again on the move.

The are heading south after Israeli forces demanded they evacuate amid an intense military assault.

They are fleeing by any means they can: on foot, in the back of trucks.

Mona al-Husseini and her family have a horse-drawn cart. She spoke to Reuters in al-Nuseirat, south of Gaza City.

"We've witnessed a lot. Many soldiers stopped us and kept searching us and stopped us for an hour. It's torture. We left the Haidar roundabout (area in Gaza City) three days ago, we were besieged there. Many rockets were fired on us and we were wrecked. I can't even talk. Our situation is hard to describe or talk about."

The fighting has expanded even as Washington pushed for a peace deal between Israel and Hamas.

Hamas says a heavy Israeli assault on Gaza City this week could wreck efforts to end the war just as negotiations have entered the home stretch.

Residents of Gaza City say this week's assault is comparable to the fiercest battle of the war.

:: October 7, 2023

Gaza City was one of the first major targets in Israel's retaliatory operation after Hamas fighters rampaged through Israeli settlements on Oct 7, killing 1,200 and taking more than 250 hostages, according to Israeli tallies.

:: October 13, 2024

A week later, Palestinians began to flee the city after Israel called on residents to evacuate.

:: January 17, 2024

By the end of 2023, an Israeli air and ground assault flattened what had been home to more than a quarter of the Gaza Strip's residents before the war.

:: May 14, 2024

As Israeli forces moved south, residents who had fled began to return. Former Gaza City residents were joined by refugees from southern cities. But Israel says Hamas fighters returned as well.

And residents such as Mona al-Husseini are again displaced.

:: Al-Nuseirat, Gaza

"This situation very, very bad. I didn't even want to leave or go to the south but necessity dictates. They forced us out, they gathered and forced us out."

Israel's assault has killed more than 38,000, according to medical authorities in Gaza.

Israeli Prime Minister Benjamin Netanyahu said on Thursday he remained committed to the Gaza ceasefire framework being negotiated, and accused the Palestinian Islamist group Hamas of making demands that contradict it.