Israel has pressed ahead with its military offensive on Gaza's second-largest city, Khan Younis, which it says is now fully encircled.
The Israel Defense Forces (IDF) said "dozens of terrorists" had been killed in the past 24 hours in Khan Younis, adding that "ground troops engaged in close-quarters combat" with militants.
In a bulletin, the United Nations humanitarian agency OCHA said Israel issued evacuation orders for a 4-square-kilometer (1.5-square-mile) part of Khan Younis, currently home to around 513,000 people and the Nasser and Al-Amal hospitals.
Palestinian President Mahmoud Abbas' office called an order for residents to head further south a "dangerous demand." He said Israel intended to "displace the Palestinian people from their homeland," according to the state-run Palestinian news agency Wafa. This, he said, would lead to "unforeseeable consequences."
Witnesses also said Israeli tanks and troops had moved into Muwasi, a coastal area of Gaza that the Israeli military had previously declared a safe zone for Palestinians.
Israel mourns dead soldiers after heavy losses
The Israeli public has been mourning the soldiers who died as the country recorded its highest troop losses in a single day.
Twenty-four Israeli soldiers were killed — 21 of them reservists who died in the Israel Defense Forces' deadliest single incident of the current operation in Gaza.
Palestinians fired a rocket at a tank that the soldiers were using as they rigged a building with explosives.
Rockets were also said to have hit the building before it and another building next to it collapsed on Monday afternoon, although confusion surrounds the precise events.
Families and friends of the dead soldiers mourned them at funerals across Israel, with coffins draped in the national flag.
Other members of the public who did not know the dead also attended, as Israeli Prime Minister Benjamin Netanyahu said an investigation had been launched into what he called a "disaster."