Dorian is battering the Abacos and Grand Bahama Islands, both in the north of the archipelago, after making landfall on Sunday night in Elbow Cay. The storm is the strongest anywhere on the planet this year, according to the US' National Hurricane Centre (NHS).
Areas of the Abaco islands were reported to be underwater after the storm hit the islands.
"Life-threatening" storm surges were expected to raise water levels as high as 18 to 23 feet above normal, producing "large and destructive" waves along the coast of both the islands, the NHS said in its latest advisory.
Dorian is forecast to lash the region overnight and through much of Monday. It was expected to reach Florida's east coast late Monday into Tuesday night.
Florida, Georgia, North and South Carolina have all declared states of emergency, the BBC reported. Evacuation orders have been given in coastal areas of Florida and South Carolina.
Bahamas residents posted footage showing floodwaters engulfing some homes after high winds had torn their roofs off.
Videos also showed capsized boats floating in floodwaters filled with debris.
Authorities closed some airports in the outlying islands, but the main international airport remained open on Sunday.
Ahead of the landfall, Bahamas Prime Minister Hubert Minnis announced an evacuation order for parts of Grand Bahama and the Abaco Islands. All tourists were asked to leave the islands.
"This is probably the most sad and worst day of my life," he told the media earlier Sunday, calling Dorian a "monster storm".
"We're facing a hurricane... One that we've never seen in the history of the Bahamas."
US President Donald Trump himself has cancelled a planned trip to Poland and met emergency management officials, reports the BBC.
He told reporters on Sunday that the storm "looks monstrous" and the US east coast "will be ultimately impacted and some of it very, very severely".
Trump has also issued a federal state of emergency for Florida, and the state's Governor, Ron DeSantis, has activated 2,000 National Guard troops, with another 2,000 on standby.
In an interview with US media on Thursday, Hubert Minnis confirmed the toll and reiterated that it was likely to rise, Efe news reported.
Dorian it hit the Bahamas on September 1 with winds of up to 298km/h -- equalling the highest ever recorded at landfall. It battered the Abaco Islands and Grand Bahama, in the north of the archipelago, for two days.
Munnis said he did not know when evacuation flights would start for people who are not elderly or sick - the first to be rescued - but he hoped it would be in five days and they would be transferred free of cost to Nassau.
Earlier, Health Minister Duane Sands had announced that 23 people had died because of Dorian, but had emphasized that the death toll would rise "much higher".
He said only a few people were qualified to officially pronounce people dead, and until deaths were officially confirmed they cannot be added to the list of victims.
If the procedure for declaring a person dead was not scrupulously followed it could have legal and insurance consequences, he added.
Sands said that specialized personnel would be sent to both islands to embalm the dead at the scene, and refrigerated containers would be provided to preserve the remains, but that these containers were beginning to run out.
The priority was to rescue people and provide urgent assistance to the elderly and the sick, who were being transferred to islands in the archipelago that were not devastated by the storm.
Sands said the country had never experienced a catastrophe of this kind.
Aid was arriving from various governments, including those of the US, the UK and Canada, as well as from neighbouring countries and the tourism sector.
Melanie Roach, with the National Emergency Management Agency, said on Thursday that about 100 people had been rescued on the Abacos and that the authorities were working to clear the roads on Grand Bahama, which were covered with debris.
Problems persist in getting aid to the entire area because of the closure of sea ports on the islands, as well as the destruction of airports.
In the wake of Hurricane Dorian, the US Coast Guard rescued 201 people in the Bahamas.
After devastating the Bahamas, Dorian was now expected to bring a "life-threatening storm surge" up the US east coast.
Residents from Florida all the way up to Virginia were warned to listen to emergency advice as the hurricane slowly moved north.
The storm killed at least 50 people, according to the official count so far, Efe news reported.
At a press conference on Wednesday, the spokesman for the National Emergency Management Agency of the Bahamas, Carl Smith, said that the death toll will surely rise.
However, he acknowledged that the 2,500 figure could come down "somewhat" as authorities catalogue all the people currently being housed in shelters on New Providence island, where the capital of Nassau is located.
Meanwhile, the Bahamas government on Wednesday rejected the "fake news" published on the social networks and by local media saying that Dorian caused thousands of deaths in the archipelago.
The head of national security for the Bahamas, Marvin Dames, told reporters on Wednesday that he was concerned by the reports that some 3,000 people had died, most of them on Abaco and Grand Bahama islands, as well as on certain keys, all of which were among the spots most heavily affected by the slow-moving and powerful storm.
He said that authorities needed to be "extremely cautious" about such news reports, since they can affect people in a very emotional way, and it can only complicate matters when exaggerated accounts of that kind circulate on the social networks.
He said he had heard that some people are claiming that the government is hiding the bodies and asked "What do we have to gain by doing that?" adding that he would like to know where those alleged bodies are so that authorities can go and recover them.
Dames added that rescue teams are continuing to meticulously inspect the areas most heavily affected by Dorian, adding that authorities can only count the bodies that they find and admitting that, due to the heavy storm surge and other flooding in the low-lying islands, some bodies may never be found.
Dorian lashed the Bahamas as a Category 5 hurricane, the most powerful on the Saffir-Simpson scale, before turning northward and moving up the eastern US coast from central Florida all the way to Canada.