However, many feared they would not be safe in Rafah either with their options for refuge dwindling, and at least nine people were killed on Wednesday in the Israeli shelling of a house in the city, Palestinian medical sources said.
Hundreds of thousands of Palestinians already fled from northern Gaza to the south during the two-month-old war between Israel and the Palestinian enclave's ruling Islamist militant movement that Israel is trying to wipe out.
The latest exodus leaves many displaced Palestinians increasingly cornered near the fortified Egyptian border, in an area that has been deemed safe by Israel's military in leaflets dropped by its aircraft as well as phone and online messages.
Israeli forces were operating in the heart of southern Gaza's largest city, Khan Younis, for the first time, its military said in a statement on Wednesday evening.
Soldiers had begun "targeted raids" in central Khan Younis, which the statement identified as a symbol of Hamas' military and administrative rule.
"The soldiers eliminated terrorists, destroyed terrorist infrastructure and located weapons."
Prime Minister Benjamin Netanyahu says Israeli forces are targeting Hamas leader Yahya Sinwar. (AP PHOTO)
Israeli Prime Minister Benjamin Netanyahu said Israeli forces were encircling the Khan Younis house of Hamas leader Yahya Al-Sinwar.
"His house may not be his fortress and he can escape but it's only a matter of time before we get him," Netanyahu said in a recorded video statement.
Khan Younis residents said Israeli tanks had neared Sinwar's home but it was not known whether he was there. Israel has said it believes many Hamas leaders and fighters are holed up in underground tunnels.
Hamas' armed wing, the al-Qassam Brigades, said combat was fierce. Residents said Israeli bombing intensified overnight, killing and wounding civilians, and that tanks were battling Palestinian militants north and east of Khan Younis.
Israeli warplanes also bombed targets across the densely populated coastal strip in one of the heaviest phases of the war in the two months since Israel began its military campaign following a deadly cross-border Hamas assault.
Hundreds of thousands of people made homeless in the north were desperately seeking shelter in the diminishing number of places in the south designated as safe areas by Israel.
The United Nations humanitarian office said in a report on Wednesday that most of the homeless people in Rafah, about 13km south of Khan Younis on the Egyptian border, were sleeping rough due to a lack of tents although the UN had managed to distribute a few hundred.
Israel unleashed its military campaign in response to a surprise October 7 incursion by Hamas fighters who rampaged through Israeli towns, killing 1200 people and seizing 240 hostages, according to Israel's tally.
Figures from Gaza's Health Ministry put the death toll in Gaza at 16,015, including 43 reported by one hospital on Tuesday and 73 by another on Wednesday.
Israel said on Wednesday 85 of its soldiers had been killed since its armoured forces invaded Gaza five weeks ago.
Displaced people driven out of the north of the Gaza Strip are now leaving clashes in Khan Younis. (AP PHOTO)
As Israel broadened its ground onslaught on Wednesday after largely taking control of north Gaza last month, Palestinian medics said Gaza's hospitals were overflowing with dead and wounded, many of them women and children, and supplies were running out.
Israel has shelled and conducted military operations in and around hospitals, such as Al Shifa Hospital in Gaza City, because it says Hamas hides fighters and command centres in them, which Hamas denies.
Israel says it seeks to protect civilians and civilian infrastructure, according to international law, though critics and even its closest ally, the US, say it needs to do more.
In Geneva, the UN human rights chief said the situation was "apocalyptic" with the risk that serious rights violations were being committed by both sides.
Leaders of the Group of Seven nations including Israel's close ally the United States called for further humanitarian truces "to address the deteriorating humanitarian crisis in Gaza and minimise civilian casualties".
The UN Security Council received a UAE-drafted resolution on Wednesday that demanded an "immediate humanitarian ceasefire" with a vote sought on Friday.
