Any Israeli ground offensive in Rafah on the Gaza border will "blow up" the hostage exchange negotiations," the Hamas-run Aqsa Television channel quoted a senior Hamas leader as saying on Sunday.
Hamas' armed wing Al-Qassam Brigades said on it Telegram channel on Sunday that Israeli strikes on Gaza during the past 96 hours "killed two Israeli hostages and seriously injured eight others."
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.
Israel says more than 130 hostages still remain in Gaza, some of them killed in Israeli strikes. The captives were taken by Hamas in the group's surprise attack in southern Israel on October 7, which it said was in retaliation to decades of Israel's Gaza blockade and ongoing aggression against the Palestinians.
The massive bombardment of Gaza which followed the attack has been ruthless, with Israel's airstrikes and ground offensive killing more than 28,000 people, mostly civilians.