Monster storm Dorian hovered over the Bahamas as surging seawaters and ferocious winds sowed chaos in low-lying island communities, killing at least five people and spurring mass evacuations on the US east coast.

Bahamas Prime Minister Hubert Minnis on Monday termed the hurricane a "historic tragedy" for the archipelago.

"Thus far, the Royal Bahamas Police Force has confirmed that there are five deaths in Abaco," Minnis told a news conference, referring to the islands where Dorian made landfall as a Category 5 storm on Sunday.

It weakened slightly to a still dangerous Category 3 storm on Tuesday, according to the National Hurricane Center (NHC).

For many, the wait for help to arrive has been terrifying.

A text message seen by AFP from a woman named Kendra Williams, who lives on Grand Bahama, said, "We are under water; we are up in the ceiling. Can someone please assist us or send some help. Please. Me and my six grandchildren and my son, we are in the ceiling."

Florida is beginning to feel the effects of Dorian, with heavy rain and "gusty winds" forecast, and the possibility of tornadoes on Tuesday, the Miami-based NHC said.

More than 9,500 people have taken cover in 121 shelters in Florida, according to the state's Division of Emergency Management.

At 07:00 GMT Tuesday, the hurricane remained stationary, the NHC said, whipping the Caribbean island with torrential rains and winds of 120 miles (195 kilometers) per hour, with higher gusts.

The NHC warned of a 12- to 18-foot storm surge above tide levels in parts of Grand Bahama, accompanied by large and destructive waves, saying that people on the island should "remain in shelter."

Water levels in the Abacos, swamped by a similar surge Sunday, were expected to slowly subside. "The hurricane will then move dangerously close to the Florida east coast late Tuesday through Wednesday evening and then move dangerously close to the Georgia and South Carolina coasts on Wednesday night and Thursday," the NHC said.

All three eastern US states have ordered coastal residents to evacuate, affecting close to a million people.

Neighboring North Carolina has also declared a state of emergency, as has Virginia further north.

Florida senator and former governor Rick Scott wrote on Twitter that "a slight wobble West" would bring the storm "on shore with devastating consequences."

"If you're in an evacuation zone, get out NOW. We can rebuild your home. We can't rebuild your life."