Bahamas National Security Minister Marvin Dames said several children were among the dead in the Atlantic archipelago and "unfortunately, we will see more deaths."
"I can't see any way out of it," the Nassau Guardian newspaper quoted Dames as telling reporters.
"This was a crisis of epic proportions," he said. "Maybe the worst that we've experienced, certainly in our lifetime."
Video footage showed catastrophic damage from the powerful hurricane on the islands of Grand Bahama and Great Abaco in the northern Bahamas including shattered homes, fields of debris and flooded streets.
The runways at Grand Bahama International Airport in Freeport, the island's largest city, were under water, complicating rescue efforts.
The US Coast Guard sent MH-60 Jayhawk helicopters to Andros Island in the southern Bahamas to help with search and rescue operations as residents trapped in their homes by floodwaters issued distress calls.
Ken Graham, director of the Miami-based National Hurricane Center (NHC), said Dorian was on the move after being "stationary for more than 24 hours battering the Bahamas."
Dorian, which has dumped as much as 30 inches (76 centimeters) of rain on the Bahamas, was downgraded Tuesday morning from a Category 3 to a Category 2 storm on the five-level wind scale.
But it remained an extremely dangerous hurricane as it crept towards the coast of the southern US states of Florida, Georgia and South and North Carolina.
A state of emergency has been declared up and down the coast for millions of US coastal residents in the path of the monster storm.
- 'Still raining' -
===================
At 11:00 am (1500 GMT), Dorian was packing maximum sustained winds of 110 miles (175 kilometers) per hour, down from 115 mph, the NHC said.
Dorian was located about 105 miles east of Fort Pierce, Florida, and moving in a northwesterly direction towards the Florida coast at a snail's pace of two mph, it said.
The NHC said Grand Bahama Island was continuing to experience dangerous winds, life-threatening storm surge and extreme flooding from the heavy rain.
The hazardous conditions would continue through much of Tuesday on Grand Bahama, which is the northernmost island in the archipelago, the NHC said.
It said Dorian was expected to pick up speed and grow in size during the day and turn towards the north on Wednesday evening.
"The hurricane will then move dangerously close to the Florida east coast late today through Wednesday evening, very near the Georgia and South Carolina coasts Wednesday night and Thursday, and near or over the North Carolina coast late Thursday and Thursday night," the NHC said.
Yasmin Rigby, a resident of Freeport, the largest city in the Bahamas, told AFP by text message on Tuesday that "most of the island is still flooded" and it was "still raining with gusty winds."
"I am still getting calls from people calling for help," Rigby said. "I cannot move from my apartment. Thankfully we have sufficient supplies."
In Coconut Grove, Florida, which has a sizeable population from the Bahamas, residents were collecting supplies for hurricane victims.
"We are looking for cases of water, canned food, can openers, flashlights, baby formula, diapers, mosquito repellent, small generators," said Nathaniel Robinson, the pastor of the Greater St Paul AME church.
Robinson said seven seaplanes were on standby to deliver the supplies "when the weather permits."
"Hopefully tomorrow," he said.
- 'Lost everything' -
=====================
Robinson said some church members have family who were "devastated by the storm."
"Some have lost everything they own," he said. "Their homes, any forms of transportation, businesses. They have absolutely nothing."
Henry Gomez, who was visiting Florida from New York, was among those dropping off supplies. "I feel bad for the Bahamas, what they're going through right now," Gomez said. "We all have to chip in and help."
Florida has started to feel the effects of Dorian, with heavy rain and strong gusts of wind reported.
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."