The area, which included the Ash Shati Refugee camp, was home to almost 300,000 Palestinians before October 7, OCHA stressed in its daily update for Monday.
"The new order covered an area of 12.43 sq km, which amounts to 3.4 percent of the total area of the Gaza Strip," OCHA added.
Some "1 per cent of the Gaza Strip have been placed under such orders‚" since Israel began issuing evacuation deadlines on December 1, OCHA added.
The residents of Gaza City in the west were told to flee south, despite large numbers of Palestinians leaving Khan Younis in recent days and dangerously overcrowded conditions in Rafah.