Aid agencies say that any assault on the city will be catastrophic in a war that has already caused untold misery.
Last week Israel rejected a Hamas proposal, saying it would not stop fighting while the group retained brigades that Israel says are hiding in Rafah.
Israeli air raids have started targeting Rafah over recent days.
On Sunday, Hamas said Israeli air raids in the Gaza Strip over the previous four days had killed two hostages and injured eight others.
The group said any Israeli assault on Rafah would "blow up" the discussions for a deal to free the remaining hostages.
Persons:
Abu Mustafa family's, we're, Laila Abu Mustafa, Benjamin Netanyahu, Abu Mustafa, Israel
Organizations:
Hamas, Sunday
Locations:
Israel, Palestinian, Rafah, Gaza, Egypt, Qatar, United States