MARSH HARBOUR, Bahamas — The U.S. humanitarian response on islands devastated by Hurricane Dorian has shifted into a new phase as desperate survivors flee the worst-hit areas of the Bahamas for towns and cities that were largely spared.

Although some remain behind, many residents of the storm-battered Abaco Islands have left for Nassau, Freeport and other areas where more assistance is available. Shelters are overflowing, and local officials have reported a surge in looting. Tens of thousands of people are believed to be homeless or in need of help.

Mark Green, the administrator of the U.S. Agency for International Development (USAID), took an aerial tour Sunday of the disaster zones, flying in a U.S. Navy Sea Stallion over flattened forests and communities reduced to rubble.

“Some places it’s like nothing happened,” he said. “Other places, it’s like they were hit by a nuclear bomb.”

The death toll remained at 44 on Sunday, but the government has warned that the number will be significantly higher when the extent of the damage becomes clearer.

The United States has provided $2.8 million in aid for the Bahamas, about a third for food and the rest for shelter, hygiene kits and other commodities, and for coordinating relief efforts. So far, 47 metric tons of supplies donated by the United States have arrived in the Bahamas, about the equivalent in size to two shipping containers. Officials said it is enough to help 44,000 people.

Much more will be needed. The immensity of the task was written on Green’s face as he stood at the open window of the helicopter, his pant legs flapping loudly in the wind several hundred feet above the Abaco Islands, where Dorian raced angrily across at 180 mph.

Acre upon acre of uprooted trees were strewn like matchsticks. Fields were flooded with stagnant water covered with green scum. Domes were blown off huge oil storage bins, exposing the slimy black liquid that remained. Rooftops were peeled away, and some houses were no more than piles of wood and other debris that no one has figured how to remove.

“We are here to help,” he told reporters at the end of his day-long trip, quickly adding, “The response will not affect the ongoing response for residents of the United States affected by Dorian.”

In meetings with Prime Minister Hubert Minnis and with charity experts in emergency relief, Green repeatedly offered assurances that the United States — from the highest levels of the administration on down — is committed to helping the island nation off the coast of Florida.

USAID has brought in Tim Callaghan to manage the U.S. relief effort in the Bahamas. Callaghan has worked for USAID for two decades and tackled some of the most difficult humanitarian challenges, including finding survivors after the 2010 earthquake in Haiti and stemming the outbreak of Ebola in Africa. Callaghan had been working in Bolivia on the effects of the fire consuming the Amazon.

Callaghan said he has rarely seen damage as severe as in the Bahamas, where Dorian made landfall last weekend as a Category 5 storm, then stalled over the Abaco Islands.

“It stood there doing this,” he said, pounding his fist into his open hand three times.

About 80 Americans involved in humanitarian aid have been on the ground since Friday. Most of them operate from a rudimentary base at what remains of a private airport on the islands.

The most pressing task is being done by 57 search-and-rescue specialists from Fairfax County who, along with a similar team from Los Angeles, regularly work for USAID following disasters around the world. They have waded through marshes in 100-degree heat, slogging on foot through pockets of mud, debris and garbage left when the high water receded. They start at sunrise and work until sundown.

Their progress is difficult to measure, in large part because their communications are severely limited.

A group called Télécoms Sans Frontières has come to help, but for now aid workers can report how they day went only after they return to the operating base.

The challenges remain mammoth. Formerly navigable channels for boats to get through were moved by the storm and have to be reopened. When flat-bottom barges get through with supplies, they are filled with survivors lining up to evacuate. The Nassau airport is overflowing with people seeking to get to the United States. Some nongovernmental groups are making plans to keep working in the Bahamas for a year or longer.

Green paid tribute to a small group of USAID workers who accompanied him to a meeting with international relief groups that have come to the Bahamas to help meet medical, food and basic survival needs.

He posed for a photograph with them, dressed like them in the unofficial but ubiquitous uniform of tan chinos and light blue polo shirts emblazoned with the slogan “USAID From the American People.”

“You are the face of American compassion,” he told them, “and we really, really appreciate it.”