Bahamas Prime Minister Hubert Minnis says at least five people have died in the Abaco Islands as Hurricane Dorian continues to pound the region as a Category 4 storm.
Minnis said there are also people in nearby Great Bahama island who are in serious distress. He said rescue crews will respond to calls for help as soon as weather conditions allow.
He said many homes and buildings have been severely damaged or destroyed.
He said: "We are in the midst of a historic tragedy."
It was the most powerful storm ever to hit the archipelago.
"Our focus right now is rescue, recovery and prayer," Minnis said on Twitter.
Hurricane Dorian's ferocious winds have weakened just a bit as the storm hovers over the Bahamas and gives the islands a merciless pounding.
With Dorian still pummelling Grand Bahama further to the west of the island chain, the Bahamas tourism and aviation ministry announced the start of rescue operations "in parts where it is safe."
"We have reports of casualties, we have reports of bodies being seen," Foreign Minister Darren Henfield said, who represents North Abaco in the Bahamian parliament.
"We cannot confirm those reports until we go out and look for ourselves."
Abaco resident Ramond King captured scenes of desolation in footage provided to AFP, showing flooded streets strewn with trees and downed power lines and at least one home washed clearly away.
"Look at this," he can be heard saying.
"We need help, everything down. Everything down. Look at my roof off, my house. I still got life. Thank God for life. I can rebuild..
"The tornado came from around this side... My neighbour used to live there. His house ain't even there."
Other footage showed Grand Bahama International Airport swamped by water.
Dorian weakened slightly on Monday to a still-devastating Category 4 storm, punishing Grand Bahama with "life-threatening storm surge and catastrophic winds," the Miami-based National Hurricane Center said.
It was grinding its way westward at a speed of 2km/h, whipping the Caribbean island with sustained winds of 240km/h.
Fear gripped residents of Freeport, as winds tore off shutters and water began coming into homes, resident Yasmin Rigby said, reached by text in the Grand Bahama island's main city.
"People who thought they were safe are now calling for help," Rigby said.
"My best friend's husband is stuck in the roof of their house with 2m water below."
Initial Red Cross estimates were that 13,000 buildings may have been damaged or destroyed by Dorian, officials in Geneva said.
Get out now
Video posted on the website of the Bahamian newspaper Tribune 242 showed water up to the roofs of wooden houses in what appeared to be a coastal town.
Capsized boats floated in muddy brown water dotted with wooden boards, tree branches and other debris.
The Miami-based National Hurricane Center forecast an 18 to 23 foot storm surge above tide levels in parts of Grand Bahama, accompanied by large and destructive waves.
Water levels in the Abacos, swamped by a similar surge Sunday, were expected to slowly subside.
"On this track, the core of extremely dangerous Hurricane Dorian will continue to pound Grand Bahama Island through much of today and tonight," the NHC said.
"The hurricane will move dangerously close to the Florida east coast late tonight through Wednesday evening, and then move dangerously close to the Georgia and South Carolina coasts on Wednesday night and Thursday."
All three eastern US states have ordered coastal residents to evacuate, affecting close to a million people.
Neighbouring North Carolina has also declared a state of emergency.
"A slight wobble West would bring this Cat 5 storm on shore with devastating consequences," said Florida Governor Rick Scott on Twitter.
"If you're in an evacuation zone, get out NOW. We can rebuild your home. We can't rebuild your life."
7-year-old drowned in flood water
A 7-year-old boy became the first victim of Hurricane Dorian in the Bahamas, where winds of up to 300km/h are ripping roofs from homes, overturning cars and tearing down power lines.
Seven-year-old Lachino Mcintosh became the first victim of the hurricane when he drowned near his family's home in Abaco, according to Bahamas Press.
The boy is reported to have lost his life while his family was trying to seek shelter. Mcintosh's sister, whose age is unknown, is also reported to be missing.
More footage posted on Facebook showed houses flooded up to their windows at Marsh Harbour, a neighbourhood on Great Abaco Island.
Another video showed a man walking through shin-deep water inside his home at Freeport on Grand Bahama.
"The house is actually sealed really well," he says, as higher floodwaters lap at his windows outside.
Where is Dorian headed next?
Hurricane Dorian is expected to continue battering Grand Bahama overnight as it tracks slowly west towards the United States.
It will then move "dangerously close" to the coast of Florida, where it's forecast to bring strong winds and "life-threatening storm surges", according to the US National Hurricane Centre (NHC).
"This thing is perilously close to the state. I think we should all hope and pray for the best, but we have to prepare that this could have major impacts on the state," the Governor of Florida, Ron DeSantis, said.
"If you look at the National Hurricane Centre's current track, I think it ends up within 48.2km of the coast of Florida. Well guess what? You do just a touch of a bump one way or another, and you have a dramatic difference all of a sudden."
Hundreds of thousands of residents have been ordered to evacuate in Florida and in the neighbouring states of Georgia and South Carolina.
"Although gradual weakening is forecast, Dorian is expected to remain a powerful hurricane during the next couple of days," the NHC warned on Monday.
Hurricane Dorian is the most powerful Atlantic hurricane to ever make landfall, equalling the Labor Day hurricane of 1935 which hit before storms were named.
The only other recorded storm that was more powerful was Hurricane Allen in 1980, with 305km/h winds, though it did not make landfall at that strength.