Hamas warned Israel that a ground offensive in Rafah, crowded with displaced Palestinians, would imperil future hostage releases.
Foreign governments, including Israel's key ally the United States, and aid groups have voiced deep concern over Israeli Prime Minister Benjamin Netanyahu's vow to extend assaults into the far-southern Gaza city.
"Any attack by the occupation army on the city of Rafah would torpedo the exchange negotiations," a Hamas leader told AFP on condition of anonymity.
Netanyahu has told troops to prepare to enter the city which now hosts more than half of Gaza's total population, spurring concern about the impact on displaced Palestinian civilians.
Biden spoke to Netanyahu on the phone Sunday and told him the Gaza advance should not go ahead in the absence of a "credible" plan to ensure "the safety" of people sheltering there, the White House said.
About 1.4 million Palestinians have crowded into Rafah, with many living in tents while food, water and medicine are becoming increasingly scarce.
Netanyahu had told US broadcaster ABC News the Rafah offensive would go ahead until Hamas is eliminated, claiming he would provide "safe passage" to civilians wishing to leave.
When pressed about where they could go, Netanyahu said: "You know, the areas that we've cleared north of Rafah, plenty of areas there. But, we are working out a detailed plan."
Mediators held new talks in Cairo for a pause in the fighting and the release of some of the 132 captives Israel says are still in Gaza, including 29 thought to be dead.
Hamas's military wing Qassam Brigades on Sunday said two hostages had been killed and eight others seriously wounded in Israeli bombardment in recent days.
Netanyahu has faced calls for early elections and mounting protests over his administration's failure to bring home the hostages.
Israeli strikes have long hit targets in Rafah, and combat on Sunday seemed intense several kilometres (miles) to the north in Khan Yunis city. AFP correspondents heard repeated explosions and saw plumes of black smoke.
Israel's military said troops were conducting "targeted raids" in the west of Khan Yunis, southern Gaza's main city, while Hamas reported violent clashes and said air strikes also hit Rafah.
Hamas said dozens of bodies had been found in Gaza City, in the coastal strip's north, after Israeli ground troops withdrew from the area.
Most of them "were martyred by bullets of snipers", the group said in a statement.
Since the start of the war, Israeli attacks also surged on the occupied West Bank.
On Sunday, troops near Bethlehem shot a man who tried to stab a soldier, the Israeli army said.
The same day, Israeli police said officers shot dead a knife-wielding suspect in the Muslim quarter of occupied East Jerusalem's Old City.