After the ceasefire came into force, Trump touted a plan to "clean out" the Gaza Strip, reiterating the idea on Monday as he called for Palestinians to move to "safer" locations such as Egypt or Jordan.
Israel had been preventing vast crowds of Palestinians from using a coastal road to return to northern Gaza, accusing Hamas of violating the truce agreement by failing to release civilian women hostages.
As the ceasefire took effect on Sunday morning, thousands of displaced, war-weary Palestinians set off across the devastated Gaza Strip to return home.
Israeli Prime Minister Benjamin Netanyahu said the deal's final details were still being worked on, but he thanked Biden for "promoting" it. Hamas leader Khalil al-Hayya said it was the result of Palestinian "resilience".
Netanyahu is facing three cases where he is alleged to have used relationships with rich, powerful men for personal and political gain, including to influence media outlets they owned or controlled.