Israel had initially focused its offensive on the north of the territory, but the occupation army has now also dropped leaflets on parts of the south, telling Palestinian civilians there to flee to other areas, but the Palestinians are running out of places to go.
Aid workers warned that the mass movement would worsen the already dire humanitarian catastrophe in the territory.
“Another wave of displacement is underway, and the humanitarian situation worsens by the hour,” the Gaza chief of the U.N. agency for Palestinian refugees, Thomas White, said in a post on X.
Israeli tanks, armored personnel carriers, and bulldozers were seen on Monday near the southern Gaza city of Khan Yunis, which is packed with civilians who fled their homes further north in the territory earlier in the war, witnesses told AFP.
An AFP journalist in Rafah near Gaza's border with Egypt saw smoke rising late Monday from buildings in southern Gaza after Israeli bombardment.
The occupation army said Monday it was taking "aggressive" action against in Khan Yunis, warning that the main road in the north and east of the city "constitutes a battlefield".
Hamas said via Telegram its militants had targeted two personnel carriers and a tank near Khan Yunis.
Its military branch also said it had fired rockets towards Beersheba in southern Israel on Tuesday, while the Israeli military said rocket warning sirens sounded there.
As Israel's brutal attacks pushes deeper into Gaza, international aid organizations have warned that civilians in the densely populated territory are running out of places to flee to.
"Nowhere is safe in Gaza and there is nowhere left to go," said Lynn Hastings, UN humanitarian coordinator for the Palestinian territories.
"If possible, an even more hellish scenario is about to unfold, one in which humanitarian operations may not be able to respond," Hastings said in a statement.
Israel has killed nearly 15,900 people in the territory, around 70 percent of them women and children.
'Like an earthquake'
In the city of Rafah near the Egyptian border, resident Abu Jahar al-Hajj said an air strike near his home felt "like an earthquake".
"Pieces of concrete started falling on us," he said.
In Deir al-Balah further to the north, Walaa Abu Libda found shelter at a hospital but said her four-year-old daughter remained trapped under rubble.
"I don't know if she is dead or alive," said Libda, one of an estimated 1.8 million people displaced in Gaza -- roughly three-quarters of the population, according to UN figures.
Three more Israeli soldiers were killed in fighting in the Gaza Strip, the army said on Tuesday, raising the number of troop deaths there to 78.
The Israeli army on Tuesday denied telling the World Health Organization to empty an aid warehouse in southern Gaza within 24 hours before ground operations in the area render it unusable.
On Monday, WHO chief Tedros Adhanom Ghebreyesus wrote on X that his organization had received a notification from the military "that we should remove our supplies from our medical warehouse in southern Gaza within 24 hours".
Israel has been targeting UN facilities, including schools used as shelters by the Palestinians which were forced to evacuate their homes.
Key ally the United States has cautioned Israel to do more to avert civilian casualties as operations shift to the south.
Speaking on condition of anonymity, senior Israeli military officials admitted that around two civilians have been killed for every dead Hamas resistance fighter in the Gaza Strip.
The occupation army claims using high-tech mapping software to track population movements inside the Gaza Strip and issue evacuation orders.
However, the UN humanitarian office OCHA has questioned the usefulness of such a tool in an area where access to telecommunications and electricity is sporadic.
On Monday, all mobile and telephone services were cut across Gaza "due to the cut-off of main fiber routes by the Israeli side", according to Palestinian telecommunications firm Paltel.
On Tuesday, global network monitor Netblocks confirmed Gaza residents were experiencing "a total loss of communications".
The latest fighting followed the collapse last Friday of a Qatar-mediated truce that saw scores of Israeli and other detainees released in exchange for Palestinian children and women prisoners.
According to the Israeli military, at least 137 captives are still being held in Gaza, but Hamas has ruled out more releases until a permanent ceasefire is agreed.
With several women still among the captives, US State Department spokesman Matthew Miller said one of the reasons why the truce fell apart could be that Hamas did not want them to "talk about what happened to them during their time" in captivity.
However, only civilian women and children held in captivity in Gaza were to be freed, under the agreement sponsored by Qatar, Egypt, and the US. However. Israel later wanted female soldiers to be released, which Hamas refused, so Israel broke the truce.
On Tuesday, the Israeli occupation army said its fighter jets had struck Hezbollah positions in response to launches on Monday from Lebanon into Israel.
The Israel-occupied West Bank has also seen a surge in violence, with 260 Palestinians killed there since the war began.