A Reuters witness saw widespread looting on Abaco, with people breaking into supermarkets and liquor stores.
Wendy Hawkes, whose home on Abaco was largely destroyed, described seeing neighbors standing outside their front doors with shotguns to ward off looters.
The relief effort faces formidable logistical challenges because of the widespread destruction caused by Dorian, which hovered over the Bahamas for nearly two days with torrential rains and fierce winds that whipped up 12- to 18-foot (3.7- to 5.5-meter) storm surges.
Dorian briefly made landfall on the Outer Banks of North Carolina on Friday with winds of 90 miles per hour (150 kph). It was heading towards Canada where it was expected to bring hurricane-force winds to parts of Nova Scotia by Saturday evening, the U.S. National Hurricane Center said.