The move comes the day after a setback on Sunday for hopes of a Gaza ceasefire.
Hamas reiterated its demand for an end to the war in exchange for the freeing of hostages.
But Israeli Prime Minister Benjamin Netanyahu flatly ruled that out.
The two sides blamed each other for the impasse and the Hamas delegation said it would leave Cairo truce talks on Sunday night to consult with its leadership.
However, the Hamas officials planned to return to the Egyptian capital on Tuesday, two Egyptian security sources said.
Israel called on civilians to evacuate parts of Rafah on Monday, our colleagues Mohammed Salem and Hatem Khaled report.
It appeared to be preparation for a long-threatened assault on Hamas holdouts in the southern Gaza Strip city where more than a million war-displaced Palestinians have been sheltering.
Instructed by Arabic text messages, telephone calls, and flyers to move to what the Israeli military called an “expanded humanitarian zone” 20 km (7 miles) away, some Palestinian families lumbered out under chilly spring rain, witnesses said.
The prospect of a high-casualty operation worries Western powers and neighbouring Egypt, which is trying to mediate a new round of truce talks between Israel and Hamas under which the Palestinian Islamist group might free some hostages.
The Rafah plan has opened an unusually public rift between Israel and Washington. Speaking to his U.S. counterpart, Israeli Defence Minister Yoav Gallant linked Monday’s operation to the deadlock in indirect diplomacy, which he blamed on Hamas.
