Any Israeli ground offensive in Rafah on the Gaza border will "blow up" the hostage exchange negotiations," Hamas-run Aqsa Television channel quoted a senior Hamas leader as saying on Sunday.
Israeli Prime Minister Benjamin Netanyahu's office said it had ordered the military to develop a plan to evacuate Rafah and destroy four Hamas battalions it says are deployed there.
Most of the displaced have sought shelter in Rafah, on the border with Egypt, but after fruitless ceasefire talks, Netanyahu this week said Israeli forces would fight on until "total victory".
Israel's military ordered civilians to flee south before previous assaults on Gaza's cities, but now there is no obvious place to go and aid agencies have said many people could die.
The conflict in Gaza began on October 7 when Hamas gunmen stormed border defences to attack Israeli towns, killing around 1,200 people, mostly civilians, and taking around 250 hostages back to Gaza, according to Israeli tallies.
Israel responded with a massive bombardment and ground offensive in which more than 28,000 Palestinians, mostly civilians, have been killed, according to medical authorities in Hamas-run Gaza.
Trump touts $5,000 payout if Republicans win as Vance waits in wings
Search expands after Philippine ferry fire kills five and leaves dozens missing
Trump says Iran war to end after US midterm elections
At least 20 killed in cargo vessel fire at China shipyard, state media reports
US military says it struck vessel in Caribbean, killing 3
At least 14 killed in explosion at weapons depot in Syria
US hits five Iranian oil tankers after attack on Navy ships
UK gives air traffic provider a week to probe outage that halted flights
