Israel’s military ordered two neighborhoods of Gaza City to evacuate on Tuesday amid signs of hunger and mounting desperation in the northern part of the enclave at a time when the focus of Israel’s offensive has shifted south.

The evacuations came as the World Food Program halted deliveries in the north on Tuesday, describing scenes of chaos as its teams faced looting, hungry crowds and gunfire in recent days.

The fiercest fighting and most intense bombing has in recent weeks shifted south to areas around Khan Younis and Rafah. But the evacuation order from Israel’s military on Tuesday for the Zaytoun and Turkoman neighborhoods of Gaza City raised the possibility of further military moves in the north.

Northern Gaza has been decimated by four months of bombardment, and continued fighting there between Israeli forces and Hamas fighters has severely hindered deliveries of aid to the estimated 300,000 people still in the area, who the United Nations has warned face starvation.

The W.F.P. had suspended its deliveries for the past three weeks because of safety concerns, and on Sunday the agency tried to restart them, but “crowds of hungry people” surrounded the initial convoy as it was going to Gaza City, and aid workers were forced to fend off people trying to climb onto the trucks, the organization said in a statement.

Another convoy on Monday “faced complete chaos and violence due to the collapse of civil order,” the statement added, saying that several trucks were looted and a driver was beaten.